On the Euler equations of incompressible fluids
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Abstract:
Euler equations of incompressible fluids use and enrich many branches of mathematics, from integrable systems to geometric analysis. They present important open physical and mathematical problems. Examples include the stable statistical behavior of ill-posed free surface problems such as the Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The paper describes some of the open problems related to the incompressible Euler equations, with emphasis on the blowup problem, the inviscid limit and anomalous dissipation. Some of the recent results on the quasigeostrophic model are also mentioned.References
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Additional Information
- Peter Constantin
- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- Email: const@math.uchicago.edu
- Received by editor(s): May 31, 2007
- Published electronically: July 5, 2007
- © Copyright 2007 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 44 (2007), 603-621
- MSC (2000): Primary 76B47; Secondary 35Q30
- DOI: https://doi.org/10.1090/S0273-0979-07-01184-6
- MathSciNet review: 2338368