Enhanced dissipation for the 2D couette flow in critical space

Nader Masmoudi, Weiren Zhao

Research output: Contribution to journalArticlepeer-review


We consider the 2 D incompressible Navier-Stokes equations on (Formula presented.) with initial vorticity that is δ close in (Formula presented.) to −1(the vorticity of the Couette flow (Formula presented.)). We prove that if (Formula presented.) 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 (Formula presented.) by a mixing-enhanced dissipation effect and then converges back to Couette flow when (Formula presented.) In particular, we show the nonlinear enhanced dissipation and the inviscid damping results in the almost critical space (Formula presented.).

Original languageEnglish (US)
Pages (from-to)1682-1701
Number of pages20
JournalCommunications in Partial Differential Equations
StatePublished - 2020


  • Couette flow; critical space; enhanced dissipation; inviscid damping, Navier Stokes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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