Non-uniqueness up to the Onsager threshold for the forced SQG equation

Abstract

We establish new non-uniqueness results for the forced inviscid surface quasi-geostrophic equation, via an alternating formulation of convex integration techniques. Our results imply non-uniquenesss in the class of weak solutions with $|\nabla|^{-1}\theta\in C_tC_x^\alpha$, for any $\alpha<1$.