##### Department of Mathematics,

University of California San Diego

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### Math 248 - Seminar in Real Analysis

## Sebastian Herr

#### Bielefeld University

## Global wellposedness of the Zakharov System below the ground state

##### Abstract:

The Zakharov system is a quadratically coupled system of a Schrödinger and a wave equation, which is related to the focussing cubic Schrödinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that it is globally well-posed in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schrödinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate. This is joint work with Timothy Candy and Kenji Nakanishi.

Host: Ioan Bejenaru

### October 18, 2022

### 11:00 AM

Zoom, contact organizers for link

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