Dong, Bo-Qing; Chen, Zhi-Min On the weak-strong uniqueness of the dissipative surface quasi-geostrophic equation. (English) Zbl 1241.35158 Nonlinearity 25, No. 5, 1513-1524 (2012). 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 \(\theta(0)=\widetilde\theta(0)\in L^2(\mathbb{R}^2)\) and the weak solution \(\theta\) is in the regular class \[ \nabla\theta\in L^r(0,T;B^0_{p,\infty}(\mathbb{R}^2))\quad\text{for }\frac 2p+\frac \alpha r=\alpha,\;\frac 2\alpha<p<\infty,\;0<\alpha\leq 2, \] then \(\theta=\widetilde\theta\) on \(\mathbb{R}^2\times[0,T]\). Cited in 10 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35D30 Weak solutions to PDEs 35Q86 PDEs in connection with geophysics PDFBibTeX XMLCite \textit{B.-Q. Dong} and \textit{Z.-M. Chen}, Nonlinearity 25, No. 5, 1513--1524 (2012; Zbl 1241.35158) Full Text: DOI