English

A direct approach to nonuniqueness and failure of compactness for the SQG equation

Analysis of PDEs 2021-07-07 v2

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.

Keywords

Cite

@article{arxiv.2007.03078,
  title  = {A direct approach to nonuniqueness and failure of compactness for the SQG equation},
  author = {Philip Isett and Andrew Ma},
  journal= {arXiv preprint arXiv:2007.03078},
  year   = {2021}
}