Remarks on the weak–strong uniqueness for the 2D quasi-geostrophic equation in BMO space

This paper is concerned with the weak–strong uniqueness of the Cauchy problem for the 2D dissipative quasi-geostrophic equation. We proved the weak–strong uniqueness when one of the two weak solutions lies in the regular class ∇θ∈L1((0,T);BMO)∇θ∈L1((0,T);BMO).