A remark on regularity criterion for the dissipative quasi-geostrophic equations. (English) Zbl 1154.76339

Summary: This paper concerns with a regularity criterion of solutions to the 2D dissipative quasi-geostrophic equations. Based on a logarithmic Sobolev inequality in Besov spaces, the absence of singularities of \(\theta \) in \([0,T]\) is derived for \(\theta \) a solution on the interval [\(0,T\)) satisfying the condition \[ \nabla^{\perp}\theta \in L^r(0,T; \dot B^0_{p,\infty})\quad \text{for} \frac{2}{p}+\frac{\alpha}{r}=\alpha,\frac{4}{\alpha} \leqslant p \leqslant \infty \] This is an extension of earlier regularity results in the Serrin’s type space \(L^r(0,T;L^p)\).


76D50 Stratification effects in viscous fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
76U05 General theory of rotating fluids
Full Text: DOI


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