Finite time singularities for a class of generalized surface quasi-geostrophic equations

Dong, Hongjie; Li, Dong

doi:10.1090/S0002-9939-08-09328-3

Finite time singularities for a class of generalized surface quasi-geostrophic equations
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by Hongjie Dong and Dong Li PDF

Proc. Amer. Math. Soc. 136 (2008), 2555-2563 Request permission

Abstract:

We propose and study a class of generalized surface quasi-geo- strophic equations. We show that in the inviscid case certain radial solutions develop gradient blow-up in finite time. In the critical dissipative case, the equations are globally well-posed with arbitrary $H^1$ initial data.

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