Non-uniqueness and convex integration for the forced Euler equations

Series
PDE Seminar
Time
Tuesday, January 17, 2023 - 3:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stan Palasek – UCLA – palasek@math.ucla.edu – https://www.math.ucla.edu/~palasek/
Organizer
Gong Chen

This talk is concerned with α-Hölder-continuous weak solutions of the incompressible Euler equations. A great deal of recent effort has led to the conclusion that the space of Euler flows is flexible when α is below 1/3, the famous Onsager regularity. We show how convex integration techniques can be extended above the Onsager regularity to all α<1/2 in the case of the forced Euler equations. This leads to a new non-uniqueness theorem for any initial data. This work is joint with Aynur Bulut and Manh Khang Huynh.