Transition threshold for the 3D Couette flow in Sobolev space

Dongyi Wei; Zhifei Zhang

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arXiv · 1803.01359

Transition threshold for the 3D Couette flow in Sobolev space

Dongyi Wei·Zhifei Zhang

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Abstract

In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number $\text{Re}$. It was proved that if the initial velocity $v_0$ satisfies $\|v_0-(y,0,0)\|_{H^2}\le c_0\text{Re}^{-1}$, then the solution of the 3D Navier-Stokes equations is global in time and does not transition away from the Couette flow. This result confirms the transition threshold conjecture in physical literatures.

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Dongyi Wei, Zhifei Zhang. 2018-03-04. Transition threshold for the 3D Couette flow in Sobolev space. https://arxiv.org/abs/1803.01359

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