Stan Palasek (UCLA): Non-uniqueness and convex integration for the forced Euler equations

This talk is concerned with the uniqueness and flexibility of C^α weak solutions of the incompressible Euler equations. A great deal of recent effort has led to the conclusion that the space of 3D Euler flows is flexible when α is below 1/3, the well-known Onsager regularity. We introduce an alternating convex integration framework for the forced Euler equations that is effective above the Onsager regularity, for all α less than 1/2. This leads to a new non-uniqueness theorem for any initial data. This work is joint with Aynur Bulut and Manh Khang Huynh.