On Pseudospectral Bound for Non-selfadjoint Operators and Its Application to Stability of Kolmogorov Flows

Slim Ibrahim, Yasunori Maekawa, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

We study the stability of the Kolmogorov flows which are stationary solutions to the two-dimensional Navier–Stokes equations in the presence of the shear external force. We establish the linear stability estimate when the viscosity coefficient ν is sufficiently small, where the enhanced dissipation is rigorously verified in the time scale O(ν-12) for solutions to the linearized problem, which has been numerically conjectured and is much shorter than the usual viscous time scale O(ν- 1). Our approach is based on the detailed analysis for the resolvent problem. We also provide the abstract framework which is applicable to the resolvent estimate for the Kolmogorov flows.

Original languageEnglish (US)
Article number14
JournalAnnals of PDE
Volume5
Issue number2
DOIs
StatePublished - Dec 1 2019

Keywords

  • Enhanced dissipation
  • Navier–Stokes equations
  • Nearly inviscid flows

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Geometry and Topology
  • Mathematical Physics
  • Physics and Astronomy(all)

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