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On pseudospectral bound for non-selfadjoint operators and its application to stability of Kolmogorov flows

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arxiv 1710.05132 v2 pith:S27SUPIH submitted 2017-10-14 math.AP

Slim Ibrahim , Yasunori Maekawa , Nader Masmoudi This is my paper · ORCID
classification math.AP
keywords flowskolmogorovstabilityestimateproblemresolventscalesolutions
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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 $\nu$ is sufficiently small, where the enhanced dissipation is rigorously verified in the time scale $O(\nu^{-\frac12})$ for solutions to the linearized problem, which has been numerically conjectured and is much shorter than the usual viscous time scale $O(\nu^{-1})$. 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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stability threshold of the 2D Couette flow in Sobolev spaces

    math.AP 2019-08 conditional novelty 8.0 of 10

    For 2D Navier-Stokes near Couette flow, H^σ vorticity perturbations of size ≤ ε Re^{-1/3} are globally stable with inviscid damping and enhanced dissipation.

  2. Stable mixing estimates in the infinite P\'eclet number limit

    math.AP 2019-09 conditional novelty 7.0 of 10

    For passive scalars in strictly monotone shear flows, the paper proves a stable mixing estimate in H^{-1} with sharp decay t^{-1} and enhanced diffusion rate ν^{1/3}, uniformly as the diffusivity ν goes to zero.

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