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

2017/10/14 by Ibrahim, Slim, Maekawa, Yasunori, Masmoudi, Nader · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.05132

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^-\frac12) 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.

Cited by

• Quantitative stability for the 2D Couette flow on the infinite channel with non-slip boundary condition
• Long-wave instability of periodic shear flows for the 2D Navier-Stokes equations
• Stability and bifurcation of Navier-Stokes equations in an annular domain with mixed boundary conditions

Related

• Pseudospectral bound and transition threshold for the 3D Kolmogorov flow
• Asymptotic stability of the Kolmogorov flow at high Reynolds numbers
• Linear stability and enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere
• Enhanced and unenhanced dampings of the Kolmogorov flow
• Bounds on Kolmogorov spectra for the Navier - Stokes equations