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Communications in Partial Differential Equations Volume 45, 2020 - Issue 12
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Research Article

Enhanced dissipation for the 2D couette flow in critical space

Nader Masmoudia NYUAD Research Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates;c Courant Institute of Mathematical Sciences, New York University, New York, NY, USACorrespondence[email protected]
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Weiren Zhaob Department of Mathematics, New York University in Abu Dhabi, Abu Dhabi, United Arab EmiratesView further author information
Pages 1682-1701 | Received 04 Sep 2019, Accepted 19 May 2020, Published online: 21 Jul 2020

Citations (17)

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Tej-Eddine Ghoul, Nader Masmoudi & Eliot Pacherie. (2023) Nonlinear enhanced dissipation in viscous Burgers type equations II. Communications in Partial Differential Equations 48:10-12, pages 1286-1322.
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Articles from other publishers (16)

Dandan Ding & Zhong Tan. (2024) Stability of the Couette flow for the two dimensional Chemotaxis-Navier–Stokes system. Nonlinear Analysis: Real World Applications 77, pages 104058.
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Hui Li, Nader Masmoudi & Weiren Zhao. (2023) A dynamical approach to the study of instability near Couette flow. Communications on Pure and Applied Mathematics 77:6, pages 2863-2946.
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Michele Dolce. (2024) Stability Threshold of the 2D Couette Flow in a Homogeneous Magnetic Field Using Symmetric Variables. Communications in Mathematical Physics 405:4.
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Binbin Shi. (2024) Suppression of blow up by mixing in generalized Keller-Segel system with fractional dissipation and strong singular kernel. Discrete and Continuous Dynamical Systems - B 0:0, pages 0-0.
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Dongyi Wei & Zhifei Zhang. (2023) Nonlinear enhanced dissipation and inviscid damping for the 2D Couette flow. Tunisian Journal of Mathematics 5:3, pages 573-592.
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Xiaoping Zhai. (2023) Linear stability analysis of the Couette flow for the two dimensional non-isentropic compressible Euler equations. Journal of Differential Equations 369, pages 215-228.
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Siming He. (2023) Enhanced Dissipation and Blow-Up Suppression in a Chemotaxis-Fluid System. SIAM Journal on Mathematical Analysis 55:4, pages 2615-2643.
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Hao Jia. (2023) Uniform Linear Inviscid Damping and Enhanced Dissipation Near Monotonic Shear Flows in High Reynolds Number Regime (I): The Whole Space Case. Journal of Mathematical Fluid Mechanics 25:3.
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Hui Li & Weiren Zhao. (2023) Metastability for the Dissipative Quasi-Geostrophic Equation and the Non-local Enhancement. Communications in Mathematical Physics 401:2, pages 1383-1415.
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Cuili ZhaiWeiren Zhao. (2023) Stability Threshold of the Couette Flow for Navier–Stokes Boussinesq System with Large Richardson Number \(\boldsymbol{\gamma}^{\boldsymbol{2}} \boldsymbol{\gt} \frac{\boldsymbol 1}{\boldsymbol 4}\). SIAM Journal on Mathematical Analysis 55:2, pages 1284-1318.
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Michele Coti Zelati, Tarek M. Elgindi & Klaus Widmayer. (2023) Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations. Archive for Rational Mechanics and Analysis 247:1.
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Sanchit Chaturvedi, Jonathan Luk & Toan Nguyen. (2023) The Vlasov–Poisson–Landau system in the weakly collisional regime. Journal of the American Mathematical Society.
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Nader Masmoudi, Cuili Zhai & Weiren Zhao. (2023) Asymptotic stability for two-dimensional Boussinesq systems around the Couette flow in a finite channel. Journal of Functional Analysis 284:1, pages 109736.
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Lan Zeng, Zhifei Zhang & Ruizhao Zi. (2022) Linear Stability of the Couette Flow in the 3D Isentropic Compressible Navier--Stokes Equations. SIAM Journal on Mathematical Analysis 54:5, pages 5698-5741.
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Nader Masmoudi, Belkacem Said-Houari & Weiren Zhao. (2022) Stability of the Couette Flow for a 2D Boussinesq System Without Thermal Diffusivity. Archive for Rational Mechanics and Analysis 245:2, pages 645-752.
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Wen Deng, Jiahong Wu & Ping Zhang. (2021) Stability of Couette flow for 2D Boussinesq system with vertical dissipation. Journal of Functional Analysis 281:12, pages 109255.
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