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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- 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
- MR Author ID: 627661
- Email: email@example.com
- Charles Fefferman
- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08540
- MR Author ID: 65640
- Email: firstname.lastname@example.org
- 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.
- © Copyright 2002 American Mathematical Society
- Journal: J. Amer. Math. Soc. 15 (2002), 665-670
- MSC (1991): Primary 76B03, 35Q30; Secondary 35Q35, 76W05
- DOI: https://doi.org/10.1090/S0894-0347-02-00394-6
- MathSciNet review: 1896236