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

Authors: Hongjie Dong and Dong Li
Journal: Proc. Amer. Math. Soc. 136 (2008), 2555-2563
MSC (2000): Primary 35Q35, 82C70
Published electronically: February 21, 2008
MathSciNet review: 2390526
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Abstract: We propose and study a class of generalized surface quasi-geostrophic 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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Additional Information

Hongjie Dong
Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912

Dong Li
Affiliation: School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540

Keywords: Mellin transform, finite-time singularities, quasi-geostrophic equations, global well-posedness.
Received by editor(s): June 11, 2007
Published electronically: February 21, 2008
Additional Notes: The authors were partially supported by the National Science Foundation under agreement No. DMS-0111298.
Communicated by: Walter Craig
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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