Authors establish enhanced dissipation and separation of time-scales for a radially symmetric linear drift-diffusion problem on R^2, with the fast mixing time-scale depending only on the flow near the origin for power-law cases, via hypocoercivity.
Transition threshold for the 3D Couette flow in Sobolev space
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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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math.AP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Separation of time-scales in drift-diffusion equations on $\mathbb{R}^2$
Authors establish enhanced dissipation and separation of time-scales for a radially symmetric linear drift-diffusion problem on R^2, with the fast mixing time-scale depending only on the flow near the origin for power-law cases, via hypocoercivity.