Stability and exponential decay for the 2D anisotropic Navier-Stokes equations with horizontal dissipation

DOI10.1007/s00021-021-00617-8zbMath1487.35287OpenAlexW3201039479WikidataQ115609516 ScholiaQ115609516MaRDI QIDQ2232920

Xiaojing Xu, Ning Zhu, Bo-Qing Dong, Jiahong Wu

Publication date: 14 October 2021

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00021-021-00617-8

zbMATH Keywords

stabilityNavier-Stokes equationspartial dissipation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations for incompressible viscous fluids (76D05) Stability in context of PDEs (35B35) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (10)

Stability of the 2D anisotropic Boussinesq equations with mixed partial dissipation ⋮ Stability for the 2D MHD equations with horizontal dissipation ⋮ Nonlinear stability for the 2D incompressible MHD system with fractional dissipation in the horizontal direction ⋮ The stability and decay for the 2D incompressible Euler-like equations ⋮ 3D anisotropic Navier–Stokes equations in T2×R  : stability and large-time behaviour ⋮ Stabilizing effect of the magnetic field and large-time behavior of 2D incompressible MHD system with vertical dissipation ⋮ Stability and exponential decay for magnetohydrodynamic equations ⋮ Global well-posedness and decay of the 2D incompressible MHD equations with horizontal magnetic diffusion ⋮ Optimal decay for the 2D anisotropic Navier-Stokes equations with mixed partial dissipation ⋮ Stability of the 3D incompressible Navier-Stokes equations with fractional horizontal dissipation

Cites Work

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• Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flow
• Exponential growth of the vorticity gradient for the Euler equation on the torus
• Small scale creation for solutions of the incompressible two-dimensional Euler equation
• Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion
• \(L^ 2\) decay for weak solutions of the Navier-Stokes equations
• Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium
• An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations
• Vorticity and Incompressible Flow
• Blowup of solutions of the unsteady Prandtl's equation
• On the decay of higher-order norms of the solutions of Navier–Stokes equations
• Double exponential growth of the vorticity gradient for the two-dimensional Euler equation

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