##### Department of Mathematics,

University of California San Diego

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### Analysis Seminar

## Jesus Oliver

#### UCSD

## A Vector Field Method for Non-Trapping, Radiating Space-Times

##### Abstract:

We study the global pointwise decay properties of solutions to the linear wave equation in 3+1 dimensions on a family time-dependent, non-trapping, radiating space-times. Assuming a local energy decay estimate we prove that sufficiently regular solutions to this equation satisfy a conformal energy estimate and higher order conformal energy estimate with one vector field. As an application we establish a global pointwise decay estimate in terms of a weighted norm on initial data.

### February 20, 2014

### 12:00 PM

### AP&M 5829

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