Elsevier

Advances in Mathematics

Volume 362, 4 March 2020, 106963
Advances in Mathematics

Linear inviscid damping and enhanced dissipation for the Kolmogorov flow

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Abstract

In this paper, we prove the linear inviscid damping and vorticity depletion phenomena for the linearized Euler equations around the Kolmogorov flow. These results confirm Bouchet and Morita's predictions based on numerical analysis. By using the wave operator method introduced by Li, Wei and Zhang, we solve Beck and Wayne's conjecture on the enhanced dissipation rate for the 2-D linearized Navier-Stokes equations around the bar state called Kolmogorov flow. The same dissipation rate is proved for the Navier-Stokes equations if the initial velocity is included in a basin of attraction of the Kolmogorov flow with the size of ν23+, here ν is the viscosity coefficient.

Keywords

Euler and Navier Stokes equation
Inviscid damping
Enhanced dissipation
Kolmogorov flow
Metastability

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