Navier–Stokes equations with external forces in Besov–Morrey spaces

References

• Fujita H, Kato T. On the nonstationary Navier-Stokes system. Arch Rational Mech Anal. 1964;16:269–315. doi: 10.1007/BF00276188
   Web of Science ®Google Scholar
• Kato T. Strong Lp-solution of the Navier-Stokes equation in Rm, with applications to weak solutions. Math Z. 1984;187:471–480. doi: 10.1007/BF01174182
   Web of Science ®Google Scholar
• Giga Y, Miyakawa T. Solutions in Lr of the Navier-Stokes initial value problem. Arch Rational Mech Anal. 1985;89:267–281. doi: 10.1007/BF00276875
   Web of Science ®Google Scholar
• Kozono H, Yamazaki M. Local and global unique solvability of the Navier-Stokes exterior problem with Cauchy data in the space Ln,∞. Houston J Math. 1995;21:755–799.
   Web of Science ®Google Scholar
• Cannone M, Planchon F. Self-similar solutions for Navier-Stokes equations in R3. Comm Partial Differ Eqn. 1996;21:179–193. doi: 10.1080/03605309608821179
   Web of Science ®Google Scholar
• Koch H, Tataru D. Well-posedness for the Navier-Stokes equations. Adv Math. 2001;157:22–35. doi: 10.1006/aima.2000.1937
   Web of Science ®Google Scholar
• Bourgain J, Pavlović N. Ill-posedness of the Navier-Stokes equations in a critical space in 3D. J Funct Anal. 2008;255:2233–2247. doi: 10.1016/j.jfa.2008.07.008
   Web of Science ®Google Scholar
• Yoneda T. Ill-posedness of the 3D-Navier-Stokes equations in Besov spaces near BMO−1. J Funct Anal. 2010;258:3376–3387. doi: 10.1016/j.jfa.2010.02.005
   Google Scholar
• Wang B. Ill-posedness for the Navier-Stokes equations in critical Besov spaces B˙∞,q−1. Adv Math. 2015;268:350–372. doi: 10.1016/j.aim.2014.09.024
   Google Scholar
• Amann H. On the strong solvability of the Navier-Stokes equations. J Math Fluid Mech. 2000;2:16–98. doi: 10.1007/s000210050018
   Web of Science ®Google Scholar
• Cannone M, Meyer Y. Littlewood-Paley decompositions and Navier-Stokes equations. Meth Appl Anal. 0000;2(3):307–319.
   Google Scholar
• Farwig R, Sohr H. Optimal initial value conditions for the existence of local strong solutions of the Navier-Stokes equations. Math Ann. 2009;345:631–642. doi: 10.1007/s00208-009-0368-y
   Web of Science ®Google Scholar
• Farwig R, Sohr H, Varnhorn W. Optimal initial value conditions for local strong solutions of the Navier-Stokes equations. Ann Univ Ferrara. 2009;55:89–110. doi: 10.1007/s11565-009-0066-4
   Google Scholar
• Cannone M, Planchon F. On the nonstationary Navier-Stokes equations with an external force. Adv Differ Eqn. 1999;4:697–730.
   Google Scholar
• Cannone M, Karch G. Smooth or singular solutions to the Navier-Stokes system. J Differ Eqn. 2004;197:247–274. doi: 10.1016/j.jde.2003.10.003
   Web of Science ®Google Scholar
• Kozono H, Shimizu S. Navier-Stokes equations with external forces in Lorentz spaces and its application to the self-similar solutions. J Math Anal Appl. 2018;458:1693–1708. doi: 10.1016/j.jmaa.2017.10.048
   Web of Science ®Google Scholar
• Kozono H, Shimizu S. Navier-Stokes equations with external forces in time-weighted Besov spaces. Math Nachr. 2018;291:1781–1800. doi: 10.1002/mana.201700078
   Web of Science ®Google Scholar
• Kashiwagi K. Well-posedness of the Navier-Stokes equations with external force in Lp space (Japanese) [master thesis of Department of Mathematics]. Shizuoka University, Graduate School of Science; 2015..
   Google Scholar
• Nakamura Y. Well-posedness of the Navier-Stokes equations with external force in homogeneous Besov space (Japanese) [master thesis of Department of Mathematics]. Shizuoka University, Graduate School of Science; 2015..
   Google Scholar
• Kozono H, Shimizu S. Strong solutions of the Navier-Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces. J Funct Anal. 2019;276:896–931. doi: 10.1016/j.jfa.2018.06.006
   Web of Science ®Google Scholar
• Cannone M. Ondelettes, paraproduits et Navier-Stokes. Paris: Diderot Editeur; 1995.
   Google Scholar
• Kozono H, Yamazaki M. Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data. Comm Partial Differ Eqn. 1994;19:959–1014. doi: 10.1080/03605309408821042
   Web of Science ®Google Scholar
• Taylor M. Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations. Comm Partial Differ Eqn. 1992;17:1407–1456. doi: 10.1080/03605309208820892
   Web of Science ®Google Scholar
• de Almeida M F, Precioso J CP. Existence and symmetries of solutions in Besov-Morrey spaces for a semilinear heat-wave type equation. J Math Anal Appl. 2015;432:338–355. doi: 10.1016/j.jmaa.2015.06.044
   Web of Science ®Google Scholar
• Kato T. Strong solutions of the Navier-Stokes equation in Morrey spaces. Bull Braz Math Soc (N.S.). 1992;22:127–155. doi: 10.1007/BF01232939
   Google Scholar
• Kozono H, Yamazaki M. The stability of small stationary solutions in Morrey spaces of the Navier-Stokes equation. Indiana Univ Math J. 1995;44:1307–1336. doi: 10.1512/iumj.1995.44.2029
   Web of Science ®Google Scholar
• Peetre J. On the theory of Lp,λ spaces. J Funct Anal. 1969;4:71–87. doi: 10.1016/0022-1236(69)90022-6
   Google Scholar
• Miyakawa T. On Morrey spaces of measures: basic properties and potential estimates. Hiroshima Math J. 1990;20:213–222. doi: 10.32917/hmj/1206454452
   Google Scholar
• Amann H. Liner and quasilinear parabolic problems, volume I abstract linear theory. Basel-Boston-Berlin: Birkhäuser-Verlag; 1995. (Monographs in Mathematics; vol. 89).
   Google Scholar
• Adams DR. Morrey spaces. Lecture Notes in Applied and Numerical Harmonic Analysis. Birkhäuser; 2015.
   Google Scholar
• Reed M, Simon B. Method of modern mathematical physics II: Fourier analysis, self-Adjointness. San Diego/New York/Berkeley/Boston/London/Sydney/ Tokyo/Toronto: Academic Press; 1975.
   Google Scholar
• Kozono H, Shimada Y. Bilnear estimates in homogeneous Triebel-Lizorkoin spaces and the Navier-Stokes equations. Math. Nachr. 2004;276:63–74. doi: 10.1002/mana.200310213
   Web of Science ®Google Scholar
• Giga Y, Sohr H. Abstract Lp estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains. J Funct Anal. 1991;102:72–94. doi: 10.1016/0022-1236(91)90136-S
   Web of Science ®Google Scholar
• Kozono H, Sohr H. Regularity criterion on weak solutions to the Navier-Stokes equations. Advances in Differential Equations. 1997;2:535–554.
   Google Scholar