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On the weak-strong uniqueness of the dissipative surface quasi-geostrophic equation. (English) Zbl 1241.35158
Summary: The weak-strong uniqueness of the dissipative surface quasi-geostrophic equation is studied. It is proved that if $\theta$ and $\widetilde\theta$ are two weak solutions of the quasi-geostrophic equation initially from the same function $\theta(0)=\widetilde\theta(0)\in L^2(\bbfR^2)$ and the weak solution $\theta$ is in the regular class $$\nabla\theta\in L^r(0,T;B^0_{p,\infty}(\bbfR^2))\quad\text{for }\frac 2p+\frac \alpha r=\alpha,\ \frac 2\alpha<p<\infty,\ 0<\alpha\le 2,$$ then $\theta=\widetilde\theta$ on $\bbfR^2\times[0,T]$.

35Q35PDEs in connection with fluid mechanics
76D05Navier-Stokes equations (fluid dynamics)
35A02Uniqueness problems for PDE: global uniqueness, local uniqueness, non-uniqueness
35D30Weak solutions of PDE
35Q86PDEs in connection with geophysics
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