##### Department of Mathematics,

University of California San Diego

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### Analysis Seminar

## Guher Camliyurt

#### USC

## Analyticity results for the Euler and Navier-Stokes equations

##### Abstract:

We revisit the preservation of analyticity and Gevrey regularity for the Euler equation. We provide a result on preservation of Gevrey norm and analyticity in Lagrangian formulation of the Euler equation and discuss the validity of the result in the Eulerian variables. Next, we consider the Navier-Stokes equations posed on the half space, with Dirichlet boundary conditions. We give a direct energy based proof for the instantaneous space-time analyticity and Gevrey class regularity of the solutions, uniformly up to the boundary of the half space.

Host: Tarek Elgindi

### May 29, 2018

### 9:45 AM

### AP&M 7321

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