##### Department of Mathematics,

University of California San Diego

****************************

### Department Colloquium

## Dallas Albritton

#### Princeton University

## Non-uniqueness of Leray solutions to the forced Navier-Stokes equations

##### Abstract:

In a seminal work, Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. Are Leray's solutions unique? This is a fundamental question in mathematical hydrodynamics, which we answer in the negative within the "forced" category, by exhibiting a one-parameter family of distinct Leray solutions with zero initial velocity and identical body force. This is joint work with Elia Brué and Maria Colombo.

Ioan Bejenaru and Andrej Zlatos

### November 4, 2022

### 4:00 PM

APM 6402

****************************