On the Euler equations of incompressible fluids

Constantin, Peter

doi:10.1090/S0273-0979-07-01184-6

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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
Posted: 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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