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.
Linear inviscid damping and enhanced dissipation for the Kolmogorov flow
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abstract
In this paper, we prove the linear inviscid damping and voticity depletion phenomena for the linearized Euler equations around the Kolmogorov flow. These results confirm Bouchet and Morita's predictions based on numerical analysis. By using the wave operator method introduced by Li, Wei and Zhang, we solve Beck and Wayne's conjecture on the optimal enhanced dissipation rate for the 2-D linearized Navier-Stokes equations around the bar state called Kolmogorov flow. The same dissipation rate is proved for the Navier-Stokes equations if the initial velocity is included in a basin of attraction of the Kolmogorov flow with the size of $\nu^{\frac 23+}$, here $\nu$ is the viscosity coefficient.
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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.