Enhanced dissipation for the 2D couette flow in critical space

• Published in: Communications in partial differential equations Vol. 45; no. 12; pp. 1682 - 1701
• Main Authors: Masmoudi, Nader, Zhao, Weiren
• Format: Journal Article
• Language: English
• 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

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...