A direct approach to nonuniqueness and failure of compactness for the SQG equation
arXiv:2007.03078 · doi:10.1088/1361-6544/abe732
Abstract
We give an alternative proof of the nonuniqueness of weak solutions to the surface quasigeostrophic equation (SQG) first shown in [Buckmaster-Shkoller-Vicol, '16]. Our approach proceeds directly at the level of the scalar field. Furthermore, we prove that every smooth scalar field with compact support that conserves the integral can be realized as a weak limit of solutions to SQG.