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Finite time singularities for a class of generalized surface quasi-geostrophic equations
Author(s):
Hongjie
Dong;
Dong
Li
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2555-2563.
MSC (2000):
Primary 35Q35, 82C70
Posted:
February 21, 2008
MathSciNet review:
2390526
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Additional information
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  initial data.
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Additional Information:
Hongjie
Dong
Affiliation:
Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
Email:
hdong@brown.edu
Dong
Li
Affiliation:
School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
Email:
dongli@math.ias.edu
DOI:
10.1090/S0002-9939-08-09328-3
PII:
S 0002-9939(08)09328-3
Keywords:
Mellin transform,
finite-time singularities,
quasi-geostrophic equations,
global well-posedness.
Received by editor(s):
June 11, 2007
Posted:
February 21, 2008
Additional Notes:
The authors were partially supported by the National Science Foundation under agreement No. DMS-0111298.
Communicated by:
Walter Craig
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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