##### Department of Mathematics,

University of California San Diego

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### MATH 248 - Analysis Seminar

## Javier Gomez-Serrano

#### Brown University and University of Barcelona

## Rigidity and flexibility of stationary solutions of the Euler equations

##### Abstract:

In this talk, I will discuss characterizations of stationary solutions of the 2D Euler equations in two different directions under different assumptions: rigidity (is every stationary solution radial?) and flexibility (do there exist non-radial stationary solutions?). The proofs will have a calculus of variations' flavor, a new observation that finite energy, stationary solutions with simply-connected vorticity have compactly supported velocity, and an application of the Nash-Moser iteration procedure. Based on joint work with Jaemin Park, Jia Shi and Yao Yao.

### March 8, 2022

### 11:00 AM

https://ucsd.zoom.us/j/

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