Lessons from Convex Integration

Philip Isett, Caltech
Fine Hall 314

In-Person Talk 

In fluid dynamics, convex integration is a method best known for its applications to proving nonuniqueness results and constructing energy non-conserving solutions.  In this talk, I will discuss how tools that arose in convex integration have applications to problems outside of this usual scope.  I will start by discussing a theoretical link between lower dimensional turbulent energy dissipation and intermittency of structure functions that was first postulated by Landau in the '40's.  I will then discuss an application to solving certain underdetermined PDE and proving related Sobolev embedding theorems.  Finally, I will discuss optimal bounds for SQG and related nonlinearities that characterize the mSQG family. 

Based on joint works with Luigi de Rosa, with Sung-Jin Oh, and with Andrew Ma.