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Growth of solutions for QG and 2D Euler equations
Author(s):
Diego
Cordoba;
Charles
Fefferman
Journal:
J. Amer. Math. Soc.
15
(2002),
665-670.
MSC (1991):
Primary 76B03, 35Q30;
Secondary 35Q35, 76W05
Posted:
February 27, 2002
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Abstract:
We study the rate of growth of sharp fronts of the Quasi-geostrophic equation and 2D incompressible Euler equations. The development of sharp fronts are due to a mechanism that piles up level sets very fast. Under a semi-uniform collapse, we obtain a lower bound on the minimum distance between the level sets.
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Additional Information:
Diego
Cordoba
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Address at time of publication:
Department of Mathematics, Princeton University, Princeton, New Jersey 08540
Email:
dcg@math.princeton.edu
Charles
Fefferman
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08540
Email:
cf@math.princeton.edu
DOI:
10.1090/S0894-0347-02-00394-6
PII:
S 0894-0347(02)00394-6
Keywords:
Quasi-geostrophic,
Euler and MHD equations,
front formation,
singularities
Received by editor(s):
March 25, 2001
Posted:
February 27, 2002
Additional Notes:
This work was initially supported by the American Institute of Mathematics.
The second author was supported in part by NSF Grant DMS 0070692.
Copyright of article:
Copyright
2002,
American Mathematical Society
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