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On the Euler equations of incompressible fluids. (English) Zbl 1132.76009
Summary: 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 Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The paper describes some of the open problems related to the incompressible Euler equations, with emphasis on the blow-up problem, the inviscid limit and anomalous dissipation. Some of the recent results on the quasigeostrophic model are also mentioned.

MSC:
76B03Existence, uniqueness, and regularity theory (fluid mechanics)
76-02Research monographs (fluid mechanics)
35Q35PDEs in connection with fluid mechanics