Enhanced dissipation for the 2D couette flow in critical space

We consider the 2 D incompressible Navier-Stokes equations on with initial vorticity that is δ close in to −1(the vorticity of the Couette flow ). We prove that if where ν denotes the viscosity, then the solution of the Navier-Stokes equation approaches some shear flow which is also close to Couette...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 45; no. 12; pp. 1682 - 1701
Main Authors Masmoudi, Nader, Zhao, Weiren
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 20.07.2020
Taylor & Francis Ltd
Subjects
Couette flow
Couette flow; critical space; enhanced dissipation; inviscid damping, Navier Stokes
Damping
Fluid dynamics
Fluid flow
Incompressible flow
Navier-Stokes equations
Shear flow
Two dimensional flow
Vorticity
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Summary:We consider the 2 D incompressible Navier-Stokes equations on with initial vorticity that is δ close in to −1(the vorticity of the Couette flow ). We prove that if where ν denotes the viscosity, then the solution of the Navier-Stokes equation approaches some shear flow which is also close to Couette flow for time by a mixing-enhanced dissipation effect and then converges back to Couette flow when In particular, we show the nonlinear enhanced dissipation and the inviscid damping results in the almost critical space
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2020.1791180