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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Growth of solutions for QG and 2D Euler equations


Authors: Diego Cordoba and Charles Fefferman
Journal: J. Amer. Math. Soc. 15 (2002), 665-670
MSC (1991): Primary 76B03, 35Q30; Secondary 35Q35, 76W05
Published electronically: February 27, 2002
MathSciNet review: 1896236
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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: http://dx.doi.org/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
Published electronically: 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.
Article copyright: © Copyright 2002 American Mathematical Society