##### Department of Mathematics,

University of California San Diego

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### Math 248 - Seminar In Real Analysis

## Hantaek Bae

#### UNIST

## Regularity and decay properties of the incompressible Navier-Stokes equations

##### Abstract:

In this talk, I will consider the incompressible Navier-Stokesequations in the mild solution setting. Using this setting, I will show how to obtain analyticity of mild solutions using the Gevrey regularity technique. This regularity enables to get decay rates of weak solutions of the Navier-Stokes equations. This idea can be applied to other dissipative equations with analytic nonlinearities. I will finally consider the regularity of the flow map of mild solutions using the Log-Lipschitz regularity of the velocity field.

Host: Tarek Elgindi

### November 7, 2017

### 8:45 AM

### AP&M 7321

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