##### Department of Mathematics,

University of California San Diego

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### Math 248 - Real Analysis

## Casey Jao

#### UCLA

## The energy-critical quintic NLS on perturbations of Euclidean space.

##### Abstract:

Consider the defocusing quintic nonlinear Schrodinger equation on $R^3$ with initial data in the energy space. This problem is "energy-critical" in view of a certain scaling invariance, which is a main source of difficulty in the analysis of this equation. It is a nontrivial fact that all finite-energy solutions scatter to linear solutions. We show that this remains true under small compact deformations of the Euclidean metric.

Host: Jacob Sterbenz

### April 19, 2016

### 10:00 AM

### AP&M 7321

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