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Original Articles

Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations

Pages 1407-1456 | Published online: 08 May 2007

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (10)

Zoran Grujić & Liaosha Xu. (2022) A regularity criterion for 3D NSE in ‘dynamically restricted’ local Morrey spaces. Applicable Analysis 101:16, pages 5809-5823.
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Boling Guo & Guoquan Qin. (2021) Navier–Stokes equations with external forces in Besov–Morrey spaces. Applicable Analysis 100:12, pages 2499-2525.
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Jacob Bedrossian & William Golding. (2021) Uniqueness criteria for the Oseen vortex in the 3d Navier-Stokes equations. Communications in Partial Differential Equations 46:6, pages 1092-1136.
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Zachary Bradshaw & Tai-Peng Tsai. (2020) Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations. Communications in Partial Differential Equations 45:9, pages 1168-1201.
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Clayton Bjorland, Lorenzo Brandolese, Dragoş Iftimie & MariaE. Schonbek. (2010) L -Solutions of the Steady-State Navier–Stokes Equations with Rough External Forces. Communications in Partial Differential Equations 36:2, pages 216-246.
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Nakao Hayashi, Naoko Ito, Elena I. Kaikina & Pavel I. Naumkin. (2005) Large time decay of solutions to Burgers type equations. Applicable Analysis 84:10, pages 1005-1024.
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Arai Hitoshi. (1997) Generalized Dirichlet Growth Theorem and Applications to Hypoelliptic and Equations. Communications in Partial Differential Equations 22:11-12, pages 2061-2088.
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M. Cannone & F Planchon. (1996) Self-similar solutions for navier-stokes equations in . Communications in Partial Differential Equations 21:1-2, pages 179-193.
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Pascal Auscher & Michael E. Taylor. (1995) Paradifferential operators and commutator estimates. Communications in Partial Differential Equations 20:9-10, pages 1743-1775.
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Hideo Kozono & Masao Yamazaki. (1994) Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data. Communications in Partial Differential Equations 19:5-6, pages 959-1014.
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Articles from other publishers (186)

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Marcelo F. de Almeida & Tiago Picon. (2024) Fourier Transform Decay of Distributions in Hardy–Morrey Spaces. Results in Mathematics 79:3.
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Tatsu-Hiko Miura. (2024) Approximation of a Solution to the Stationary Navier–Stokes Equations in a Curved Thin Domain by a Solution to Thin-Film Limit Equations. Journal of Mathematical Fluid Mechanics 26:2.
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Diego Chamorro & Gastón Vergara-Hermosilla. (2024) Lebesgue spaces with variable exponent: some applications to the Navier–Stokes equations. Positivity 28:2.
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Li Peng & Yong Zhou. (2023) The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations. Qualitative Theory of Dynamical Systems 23:1.
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Xuan-Xuan Xi, Yong Zhou & Mimi Hou. (2023) Well-Posedness of Mild Solutions for the Fractional Navier–Stokes Equations in Besov Spaces. Qualitative Theory of Dynamical Systems 23:1.
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Hajime Koba. (2023) On generalized compressible fluid systems on an evolving surface with a boundary. Quarterly of Applied Mathematics 81:4, pages 721-749.
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Jan W. Cholewa & Aníbal Rodríguez-Bernal. (2023) On linear higher-order parabolic equations in Morrey spaces. Analysis and Applications 21:06, pages 1561-1608.
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Hajime Koba. (2023) Thermodynamical Modeling of Multiphase Flow System with Surface Tension and Flow. Mathematical Modelling of Natural Phenomena 18, pages 32.
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Tatsu-Hiko Miura. (2022) Linear stability and enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere. Journal of Functional Analysis 283:8, pages 109607.
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Arnold Reusken. (2022) Analysis of finite element methods for surface vector-Laplace eigenproblems. Mathematics of Computation 91:336, pages 1587-1623.
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Yanqing Wang, Quansen Jiu & Wei Wei. (2022) Leray's Backward Self-Similar Solutions to the 3D Navier--Stokes Equations in Morrey Spaces. SIAM Journal on Mathematical Analysis 54:3, pages 2768-2791.
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Yao Yang & Junming Liu. (2022) Integral Operators on Bergman–Morrey Spaces. The Journal of Geometric Analysis 32:6.
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Qianjun He, Xinfeng Wu & Dunyan Yan. (2022) Bounds for Multilinear Operators under an Integral Type Condition on Morrey Spaces. Acta Mathematica Scientia 42:3, pages 1191-1208.
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Feng Liu, Shuai Xi, Zirong Zeng & Shengguo Zhu. (2022) Global mild solutions to three-dimensional magnetohydrodynamic equations in Morrey spaces. Journal of Differential Equations 314, pages 752-807.
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Jan W. Cholewa & Anibal Rodriguez-Bernal. (2020) Sharp estimates for homogeneous semigroups in homogeneous spaces. Applications to PDEs and fractional diffusion in ℝN. Communications in Contemporary Mathematics 24:01.
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Kieu Huu Dung, Do Lu Cong Minh & Pham Thi Kim Thuy. (2022) Commutators of Hardy-Cesàro operators on Morrey-Herz spaces with variable exponents. AIMS Mathematics 7:10, pages 19147-19166.
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Taiki Takeuchi. (2021) Maximal Lorentz regularity for the Keller–Segel system of parabolic–elliptic type. Journal of Evolution Equations 21:4, pages 4619-4640.
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Takeshi Suguro. (2021) Well-posedness and unconditional uniqueness of mild solutions to the Keller–Segel system in uniformly local spaces. Journal of Evolution Equations 21:4, pages 4599-4618.
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Kyungkeun Kang, Hideyuki Miura & Tai-Peng Tsai. (2021) Regular sets and an 𝜖-regularity theorem in terms of initial data for the Navier–Stokes equations. Pure and Applied Analysis 3:3, pages 567-594.
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Taiki Takeuchi. (2021) The Keller-Segel system of parabolic-parabolic type in homogeneous Besov spaces framework. Journal of Differential Equations 298, pages 609-640.
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Rza Mustafayev & Abdulhamit Kucukaslan. (2021) An extension of the Muckenhoupt–Wheeden theorem to generalized weighted Morrey spaces. Georgian Mathematical Journal 28:4, pages 595-610.
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Tatsu-Hiko Miura. (2020) Navier–Stokes Equations in a Curved Thin Domain, Part II: Global Existence of a Strong Solution. Journal of Mathematical Fluid Mechanics 23:1.
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Jingjing Zhang & Ting Zhang. (2021) Local well-posedness of perturbed Navier-Stokes system around Landau solutions. Electronic Research Archive 29:4, pages 2719-2739.
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Jinyi Sun, Zunwei Fu, Yue Yin & Minghua Yang. (2021) Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces. Discrete & Continuous Dynamical Systems - B 26:6, pages 3409.
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Muhammad Zainul Abidin & Jiecheng Chen. (2020) Global well-posedness for fractional Navier-Stokes equations in variable exponent Fourier-Besov-Morrey spaces. Acta Mathematica Scientia 41:1, pages 164-176.
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Abelardo Duarte-Rodríguez, Lucas C. F. Ferreira & Élder J. Villamizar-Roa. (2020) Global Existence for an Attraction–Repulsion Chemotaxis-Fluid System in a Framework of Besov–Morrey type. Journal of Mathematical Fluid Mechanics 22:4.
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Hua Wang. (2020) Semigroup Maximal Functions, Riesz Transforms, and Morrey Spaces Associated with Schrödinger Operators on the Heisenberg Groups. Journal of Function Spaces 2020, pages 1-22.
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Philip Brandner & Arnold Reusken. (2020) Finite element error analysis of surface Stokes equations in stream function formulation. ESAIM: Mathematical Modelling and Numerical Analysis 54:6, pages 2069-2097.
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Andrea Scapellato. (2020) A Modified Spanne–Peetre Inequality on Mixed Morrey Spaces. Bulletin of the Malaysian Mathematical Sciences Society 43:6, pages 4197-4206.
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Leanne Dong. (2020) Strong solutions for the stochastic Navier-Stokes equations on the 2D rotating sphere with stable Lévy noise. Journal of Mathematical Analysis and Applications 489:2, pages 124182.
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Hua Wang. (2020) Morrey spaces for Schrödinger operators with certain nonnegative potentials, Littlewood–Paley and Lusin functions on the Heisenberg groups. Banach Journal of Mathematical Analysis 14:4, pages 1532-1557.
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Abdulhamit Kucukaslan. (2020) Equivalence of norms of the generalized fractional integral operator and the generalized fractional maximal operator on the generalized weighted Morrey spaces. Annals of Functional Analysis 11:4, pages 1007-1026.
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Guoquan Qin. (2020) Existence and large time behavior to the nematic liquid crystal equations in Besov-Morrey spaces. Journal of Mathematical Analysis and Applications 486:1, pages 123884.
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Dorothee D. Haroske & Leszek Skrzypczak. (2019) Morrey Sequence Spaces: Pitt’s Theorem and Compact Embeddings. Constructive Approximation 51:3, pages 505-535.
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Tuoc Phan. (2019) Well-posedness for the Navier–Stokes equations in critical mixed-norm Lebesgue spaces. Journal of Evolution Equations 20:2, pages 553-576.
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T Koide & T Kodama. (2020) Variational formulation of compressible hydrodynamics in curved spacetime and symmetry of stress tensor. Journal of Physics A: Mathematical and Theoretical 53:21, pages 215701.
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Nguyen Minh Chuong, Dao Van Duong & Kieu Huu Dung. (2019) Maximal operators and singular integrals on the weighted Lorentz and Morrey spaces. Journal of Pseudo-Differential Operators and Applications 11:1, pages 201-228.
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Hua Wang. (2020) Morrey spaces for Schrödinger operators with nonnegative potentials, fractional integral operators and the Adams inequality on the Heisenberg groups. Journal of Mathematical Analysis and Applications 482:1, pages 123523.
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Lucas C. F. Ferreira & Jhean E. Pérez-López. (2019) Bilinear estimates and uniqueness for Navier–Stokes equations in critical Besov-type spaces. Annali di Matematica Pura ed Applicata (1923 -) 199:1, pages 379-400.
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Arnold Reusken. (2020) Stream function formulation of surface Stokes equations. IMA Journal of Numerical Analysis 40:1, pages 109-139.
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Piotr Biler, Grzegorz Karch & Dominika Pilarczyk. (2019) Global radial solutions in classical Keller–Segel model of chemotaxis. Journal of Differential Equations 267:11, pages 6352-6369.
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Azzeddine El Baraka & Mohamed Toumlilin. (2019) Well-Posedness and Stability for the Generalized Incompressible Magneto-Hydrodynamic Equations in Critical Fourier-Besov-Morrey Spaces. Acta Mathematica Scientia 39:6, pages 1551-1567.
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Kuijie Li & Baoxiang Wang. (2019) Blowup criterion for Navier–Stokes equation in critical Besov space with spatial dimensions d ≥ 4. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36:6, pages 1679-1707.
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Kwok-Pun Ho. (2019) Weak Type Estimates of Singular Integral Operators on Morrey–Banach Spaces. Integral Equations and Operator Theory 91:3.
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Minghua Yang, Zunwei Fu & Jinyi Sun. (2019) Existence and large time behavior to coupled chemotaxis-fluid equations in Besov–Morrey spaces. Journal of Differential Equations 266:9, pages 5867-5894.
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Piotr Biler & Dominika Pilarczyk. (2019) Around a singular solution of a nonlocal nonlinear heat equation. Nonlinear Differential Equations and Applications NoDEA 26:1.
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Jing Zhang & Huoxiong Wu. (2018) Variation Inequalities Related to Schrödinger Operators on Morrey Spaces. Chinese Annals of Mathematics, Series B 39:6, pages 973-988.
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Piotr Biler. (2018) Mathematical Challenges in the Theory of Chemotaxis. Annales Mathematicae Silesianae 32:1, pages 43-63.
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Tatsu-Hiko Miura. (2017) On singular limit equations for incompressible fluids in moving thin domains. Quarterly of Applied Mathematics 76:2, pages 215-251.
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Hajime Koba. (2017) On derivation of compressible fluid systems on an evolving surface. Quarterly of Applied Mathematics 76:2, pages 303-359.
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Piero D’Ancona & Renato Lucà. (2017) Stability Properties of the Regular Set for the Navier–Stokes Equation. Journal of Mathematical Fluid Mechanics 20:2, pages 819-852.
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Lucas C. F. Ferreira & Jhean E. Pérez-López. (2018) Besov-weak-Herz spaces and global solutions for Navier–Stokes equations. Pacific Journal of Mathematics 296:1, pages 57-77.
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Yanping Chen & Yong Ding. (2018) Commutators of the fractional integrals for second-order elliptic operators on Morrey spaces. Forum Mathematicum 30:3, pages 617-629.
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Piotr Biler, Grzegorz Karch & Jacek Zienkiewicz. (2018) Large global-in-time solutions to a nonlocal model of chemotaxis. Advances in Mathematics 330, pages 834-875.
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Dorothee D. Haroske, Cornelia Schneider & Leszek Skrzypczak. (2017) Morrey Spaces on Domains: Different Approaches and Growth Envelopes. The Journal of Geometric Analysis 28:2, pages 817-841.
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Z. Brzeźniak, B. Goldys & Q. T. Le Gia. (2017) Random Attractors for the Stochastic Navier–Stokes Equations on the 2D Unit Sphere. Journal of Mathematical Fluid Mechanics 20:1, pages 227-253.
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T. Barker. (2017) Uniqueness Results for Weak Leray–Hopf Solutions of the Navier–Stokes System with Initial Values in Critical Spaces. Journal of Mathematical Fluid Mechanics 20:1, pages 133-160.
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Maxim A. Olshanskii, Annalisa Quaini, Arnold Reusken & Vladimir Yushutin. (2018) A Finite Element Method for the Surface Stokes Problem. SIAM Journal on Scientific Computing 40:4, pages A2492-A2518.
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Sven Gross, Thomas Jankuhn, Maxim A. Olshanskii & Arnold Reusken. (2018) A Trace Finite Element Method for Vector-Laplacians on Surfaces. SIAM Journal on Numerical Analysis 56:4, pages 2406-2429.
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Marcelo F. de Almeida, Lucas C. F. Ferreira & Lidiane S. M. Lima. (2017) Uniform global well-posedness of the Navier–Stokes–Coriolis system in a new critical space. Mathematische Zeitschrift 287:3-4, pages 735-750.
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Viorel Barbu & Michael Röckner. (2017) Global solutions to random 3D vorticity equations for small initial data. Journal of Differential Equations 263:9, pages 5395-5411.
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Chi Hin Chan, Magdalena Czubak & Marcelo M. Disconzi. (2017) The formulation of the Navier–Stokes equations on Riemannian manifolds. Journal of Geometry and Physics 121, pages 335-346.
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Nguyen Anh Dao & Quoc-Hung Nguyen. (2017) Nonstationary Navier–Stokes equations with singular time-dependent external forces. Comptes Rendus. Mathématique 355:9, pages 966-972.
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Yong Zhou, Li Peng, Bashir Ahmad & Ahmed Alsaedi. (2017) Energy methods for fractional Navier–Stokes equations. Chaos, Solitons & Fractals 102, pages 78-85.
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Dao Quang Khai. (2016) Well-Posedness for the Navier-Stokes Equations with Datum in the Sobolev Spaces. Acta Mathematica Vietnamica 42:3, pages 431-443.
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Yu-Zhu Wang, Liuxin Gu & Yinxia Wang. (2017) Decay estimate of global solutions to the generalized double dispersion model in Morrey spaces. Zeitschrift für angewandte Mathematik und Physik 68:4.
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Azzeddine El Baraka & Mohamed Toumlilin. (2017) Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces. Moroccan Journal of Pure and Applied Analysis 3:1, pages 1-13.
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Hajime Koba, Chun Liu & Yoshikazu Giga. (2016) Energetic variational approaches for incompressible fluid systems on an evolving surface. Quarterly of Applied Mathematics 75:2, pages 359-389.
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Philippe Souplet. (2017) Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in . Journal of Functional Analysis 272:5, pages 2005-2037.
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Yuzhao Wang & Jie Xiao. (2017) Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces. Advances in Nonlinear Analysis 8:1, pages 203-224.
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D.Q. Khai & N.M. Tri. (2017) Well-posedness for the Navier–Stokes equations with data in homogeneous Sobolev–Lorentz spaces. Nonlinear Analysis: Theory, Methods & Applications 149, pages 130-145.
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Qixiang Yang & Pengtao Li. (2016) Regular Wavelets, Heat Semigroup and Application to the Magneto-hydrodynamic Equations with Data in Critical Triebel-Lizorkin Type Oscillation Spaces. Taiwanese Journal of Mathematics 20:6.
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Yanping Chen, Yong Ding & Guixiang Hong. (2016) Commutators with fractional differentiation and new characterizations of BMO-Sobolev spaces. Analysis & PDE 9:6, pages 1497-1522.
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Simon Blatt & Michael Struwe. (2016) Well-posedness of the supercritical Lane–Emden heat flow in Morrey spaces. ESAIM: Control, Optimisation and Calculus of Variations 22:4, pages 1370-1381.
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Renjin Jiang, Jie Xiao & Dachun Yang. (2016) Towards spaces of harmonic functions with traces in square Campanato spaces and their scaling invariants. Analysis and Applications 14:05, pages 679-703.
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Piero D’Ancona & Renato Lucà. (2016) On the Regularity Set and Angular Integrability for the Navier–Stokes Equation. Archive for Rational Mechanics and Analysis 221:3, pages 1255-1284.
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Suzhen Mao & Huoxiong Wu. (2016) CHARACTERIZATION OF FUNCTIONS VIA COMMUTATORS OF BILINEAR FRACTIONAL INTEGRALS ON MORREY SPACES. Bulletin of the Korean Mathematical Society 53:4, pages 1071-1085.
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D.Q. Khai & N.M. Tri. (2016) Well-posedness for the Navier–Stokes equations with datum in Sobolev–Fourier–Lorentz spaces. Journal of Mathematical Analysis and Applications 437:2, pages 754-781.
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Minghua Yang & Jinyi Sun. (2016) Existence and asymptotic behavior to the incompressible nematic liquid crystal flow in the whole space. Mathematical Methods in the Applied Sciences 39:7, pages 1836-1854.
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Pierre Lemarie-Rieusset. 2016. The Navier-Stokes Problem in the 21st Century. The Navier-Stokes Problem in the 21st Century 677 708 .
Lucas C. F. Ferreira. (2016) On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier–Stokes equations. Journal de Mathématiques Pures et Appliquées 105:2, pages 228-247.
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Renato Lucà. (2016) On the size of the regular set of suitable weak solutions of the Navier–Stokes equation. Journées équations aux dérivées partielles, pages 1-14.
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Minghua Yang. (2015) On analyticity rate estimates to the magneto-hydrodynamic equations in Besov-Morrey spaces. Boundary Value Problems 2015:1.
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Marcelo F. de Almeida & Juliana C.P. Precioso. (2015) Existence and symmetries of solutions in Besov–Morrey spaces for a semilinear heat-wave type equation. Journal of Mathematical Analysis and Applications 432:1, pages 338-355.
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Qiao Liu. (2014) A Regularity Criterion for the Navier-Stokes Equations in Terms of One Directional Derivative of the Velocity. Acta Applicandae Mathematicae 140:1, pages 1-9.
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Junming Liu & Zengjian Lou. (2015) Properties of analytic Morrey spaces and applications. Mathematische Nachrichten 288:14-15, pages 1673-1693.
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Wen Yuan, Winfried Sickel & DaChun Yang. (2015) Interpolation of Morrey-Campanato and related smoothness spaces. Science China Mathematics 58:9, pages 1835-1908.
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Junyu Lin, Baishun Lai & Changyou Wang. (2014) Global well-posedness of the Landau–Lifshitz–Gilbert equation for initial data in Morrey spaces. Calculus of Variations and Partial Differential Equations 54:1, pages 665-692.
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Omar Lazar. (2015) Global and Local Existence for the Dissipative Critical SQG Equation with Small Oscillations. Journal of Mathematical Fluid Mechanics 17:3, pages 533-549.
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Z. Brzeźniak, B. Goldys & Q.T. Le Gia. (2015) Random dynamical systems generated by stochastic Navier–Stokes equations on a rotating sphere. Journal of Mathematical Analysis and Applications 426:1, pages 505-545.
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Yong Ding & Ting Mei. (2014) Boundedness and Compactness for the Commutators of Bilinear Operators on Morrey Spaces. Potential Analysis 42:3, pages 717-748.
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Yanping Chen & Kai Zhu. (2015) Weighted norm inequality for the singular integral with variable kernel and fractional differentiation. Journal of Mathematical Analysis and Applications 423:2, pages 1610-1629.
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V. S. Guliyev, A. F. Ismayilova, A. Kucukaslan & A. Serbetci. (2015) Generalized Fractional Integral Operators on Generalized Local Morrey Spaces. Journal of Function Spaces 2015, pages 1-8.
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Hao Feng & Vladimír Šverák. (2014) On the Cauchy Problem for Axi-Symmetric Vortex Rings. Archive for Rational Mechanics and Analysis 215:1, pages 89-123.
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Lucas C. F. Ferreira & Lidiane S. M. Lima. (2014) Self-similar solutions for active scalar equations in Fourier–Besov–Morrey spaces. Monatshefte für Mathematik 175:4, pages 491-509.
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Anne-Laure Dalibard & Christophe Prange. (2014) Well-posedness of the Stokes–Coriolis system in the half-space over a rough surface. Analysis & PDE 7:6, pages 1253-1315.
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D.Q. Khai & N.M. Tri. (2014) Solutions in mixed-norm Sobolev–Lorentz spaces to the initial value problem for the Navier–Stokes equations. Journal of Mathematical Analysis and Applications 417:2, pages 819-833.
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PengTao Li, JunMing Liu & ZengJian Lou. (2014) Integral operators on analytic Morrey spaces. Science China Mathematics 57:9, pages 1961-1974.
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Renato Lucà. (2014) Regularity criteria with angular integrability for the Navier–Stokes equation. Nonlinear Analysis: Theory, Methods & Applications 105, pages 24-40.
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Giampiero Palatucci & Adriano Pisante. (2013) Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces. Calculus of Variations and Partial Differential Equations 50:3-4, pages 799-829.
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Zujin Zhang, Tong Tang & Fumin Zhang. (2014) A Remark on the Regularity Criterion for the MHD Equations via Two Components in Morrey-Campanato Spaces. Journal of Difference Equations 2014, pages 1-4.
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Zujin Zhang. (2014) A Remark on the Regularity Criterion for the 3D Boussinesq Equations Involving the Pressure Gradient. Abstract and Applied Analysis 2014, pages 1-4.
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Lucas C. F. Ferreira & Juliana C. Precioso. (2013) Existence of solutions for the 3D-micropolar fluid system with initial data in Besov–Morrey spaces. Zeitschrift für angewandte Mathematik und Physik 64:6, pages 1699-1710.
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Marcelo Fernandes de Almeida & Lucas C.F. Ferreira. (2013) On the local solvability in Morrey spaces of the Navier–Stokes equations in a rotating frame. Journal of Mathematical Analysis and Applications 405:2, pages 362-372.
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Tuoc Van Phan & Nguyen Cong Phuc. (2013) Stationary Navier–Stokes equations with critically singular external forces: Existence and stability results. Advances in Mathematics 241, pages 137-161.
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V. S. Guliyev, A. Eroglu & Y. Y. Mammadov. (2013) Riesz potential in generalized Morrey spaces on the Heisenberg group. Journal of Mathematical Sciences 189:3, pages 365-382.
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