##### Department of Mathematics,

University of California San Diego

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### Math 248 - Analysis Seminar

## Yu Deng

#### USC

## Instability of the Couette flow in low regularity spaces

##### Abstract:

In an exciting paper, J. Bedrossian and N. Masmoudi established the stability of the 2D Couette flow in Gevrey spaces of index greater than 1/2. I will talk about recent joint work with N. Masmoudi, which proves, in the opposite direction, the instability of the Couette flow in Gevrey spaces of index smaller than 1/2. This confirms, to a large extent, that the transient growth predicted heuristically in earlier works does exist and has the expected strength. The proof is based on the framework of the stability result, with a few crucial new observations. I will also discuss related works regarding Landau damping, and possible extensions to infinite time.

Host: Tarek Elgindi

### November 6, 2018

### 8:45 AM

### AP&M 7321

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