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Global well-posedness for a modified critical dissipative quasi-geostrophic equation. (English) Zbl 05986533

Summary: We consider the following modified quasi-geostrophic equation

t δ+u·θ+ν|D| α θ=0,u=|D| α-1 θ,x 2

with ν>0 and α]0,1[]1,2[. When α]0,1[, the equation was firstly introduced by Constantin, Iyer and Wu (2008) in [11]. Here, by using the modulus of continuity method, we prove the global well-posedness of the system. As a byproduct, we also show that for every α]0,2[, the Lipschitz norm of the solution has a uniform exponential upper bound.

MSC:
76U05Rotating fluids
76B03Existence, uniqueness, and regularity theory (fluid mechanics)
35Q35PDEs in connection with fluid mechanics
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