Uniqueness of weak L2 solutions

Determine whether weak L2 solutions of the dissipative surface quasi-geostrophic equation are unique.

Background

The introduction reviews earlier existence results for weak solutions of the SQG equation, including global weak solutions in L² and in negative-order Sobolev spaces. Although the paper proves existence of global weak solutions for the broader gSQG family in H^{α/2−1}, it does not resolve uniqueness for weak L² solutions. The paper also notes nonuniqueness results for certain classes of solutions with negative Sobolev regularity, which further motivates the unresolved uniqueness question.