##### Department of Mathematics,

University of California San Diego

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### Analysis Seminar

## Hao Jia

#### University of Minnesota

## Channel of energy inequality and absence of null concentration of energy for wave map equations

##### Abstract:

Wave maps are natural hyperbolic analogue of harmonic maps. The study of the wave maps over the last twenty plus years has led to many beautiful and deep ideas, culminating in the proof of the ``ground state conjecture'' by Sterbenz and Tataru (with independent proof by Tao, and by Krieger&Schlag when the map has hyperbolic plane as target). The understanding of wave maps is now quite satisfactory. There are however still some remaining interesting problems, involving more detailed dynamics of wave maps. In this talk, we shall look at the problem of ruling out the so called ``null concentration of energy'' for wave maps. We will briefly review the history of wave maps, and explain why the null concentration of energy is relevant, and why the channel of energy inequality seems to be uniquely good in ruling out such possible energy concentration in the presence of solitons.

Host: Tarek Elgindi

### February 27, 2018

### 8:45 AM

### AP&M 7321

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