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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have