Bulletin of the American Mathematical Society

Author(s): Peter Constantin
Journal: Bull. Amer. Math. Soc. 44 (2007), 603-621.
MSC (2000): Primary 76B47; Secondary 35Q30
Posted: July 5, 2007
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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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Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 76B47, 35Q30

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

DOI: 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
Posted: July 5, 2007
Copyright of article: Copyright 2007, American Mathematical Society

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