Enhanced dissipation for the 2D couette flow in critical space
Nader Masmoudi, Weiren Zhao
Abstract
We consider the 2 D incompressible Navier-Stokes equations on T×R, with initial vorticity that is δ close in HxlogLy2 to −1(the vorticity of the Couette flow (y,0)). We prove that if δ≪ν1/2, 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 t≫ν−1/3 by a mixing-enhanced dissipation effect and then converges back to Couette flow when t→+∞. In particular, we show the nonlinear enhanced dissipation and the inviscid damping results in the almost critical space HxlogLy2⊂Lx,y2.
Topics & Concepts
Couette flowInviscid flowVorticityDissipationFlow (mathematics)Taylor–Couette flowMathematicsShear flowNavier–Stokes equationsMixing (physics)CompressibilityNonlinear systemSpace (punctuation)Classical mechanicsPhysicsMechanicsThermodynamicsVortexQuantum mechanicsPhilosophyLinguisticsFluid Dynamics and Turbulent FlowsNavier-Stokes equation solutionsStochastic processes and financial applications