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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 θ in [0,T] is derived for θ a solution on the interval [0,T) satisfying the condition

θL r (0,T;B ˙ p, 0 )for2 p+α r=α,4 αp

This is an extension of earlier regularity results in the Serrin’s type space L r (0,T;L p ).

MSC:
76D50Stratification effects in viscous fluids
76D03Existence, uniqueness, and regularity theory
35Q35PDEs in connection with fluid mechanics
76U05Rotating fluids