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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

On the Euler equations of incompressible fluids


Author: Peter Constantin
Journal: Bull. Amer. Math. Soc. 44 (2007), 603-621
MSC (2000): Primary 76B47; Secondary 35Q30
Published electronically: July 5, 2007
MathSciNet review: 2338368
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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.


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Additional Information

Peter Constantin
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: const@math.uchicago.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-07-01184-6
PII: S 0273-0979(07)01184-6
Keywords: Euler, anomalous dissipation, blowup, free surface, quasigeostrophic equation, vanishing viscosity, blowup, ill-posed, turbulence
Received by editor(s): May 31, 2007
Published electronically: July 5, 2007
Article copyright: © Copyright 2007 American Mathematical Society