Weak-strong uniqueness criterion for the beta -generalized surface quasi-geostrophic equation

摘要

We prove that weak-strong uniqueness holds for the (beta )-generalized surface quasi-geostrophic equation in the regular class (nabla theta in L^{q}(0,T; L^{p}(mathbb{R }^{2}))) with (frac{alpha }{q}+frac{2}{p}=alpha +beta -1), where (alpha in (0,1], beta in [1,2)) and (frac{2}{alpha +beta -1}