Linear inviscid damping and enhanced dissipation for the Kolmogorov flow

Dongyi Wei, Zhifei Zhang, Weiren Zhao

Research output: Contribution to journalArticle

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 [Formula presented], here ν is the viscosity coefficient.

Original languageEnglish (US)
Article number106963
JournalAdvances in Mathematics
Volume362
DOIs
StatePublished - Mar 4 2020

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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