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 $$O(\nu ^{-\frac{1}{2}})$$ 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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