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arXiv · 1908.11042

Stability threshold of the 2D Couette flow in Sobolev spaces

Nader Masmoudi·Weiren Zhao
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Abstract

We study the stability threshold of the 2D Couette flow in Sobolev spaces at high Reynolds number $Re$. We prove that if the initial vorticity $\Omega_{in}$ satisfies $\|\Omega_{in}-(-1)\|_{H^{\sigma}}\leq \epsilon Re^{-1/3}$, then the solution of the 2D Navier-Stokes equation approaches to some shear flow which is also close to Couette flow for time $t\gg Re^{1/3}$ by a mixing-enhanced dissipation effect and then converges back to Couette flow when $t\to +\infty$.

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Nader Masmoudi, Weiren Zhao. 2019-08-29. Stability threshold of the 2D Couette flow in Sobolev spaces. https://doi.org/10.4171/aihpc/8

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