##### Department of Mathematics,

University of California San Diego

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### Math 248 - Seminar In Real Analysis

## In-Jee Jeong

#### Princeton University

## Finite time blow-up for strong solutions to the 3D Euler equations

##### Abstract:

We show finite time blow-up for strong solutions to the 3D Euler equations on the exterior of a cone. The solutions we construct has finite energy, and velocity is axisymmetric and Lipschitz continuous before the blow up time. We achieve this by first analyzing scale-invariant (radially homogeneous) solutions, whose dynamics is governed by a 1D system. Then we make a cut-off argument to ensure finiteness of energy.

Host: Tarek Elgindi

### October 31, 2017

### 9:45 AM

### AP&M 7321

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