Euler equations for incompressible ideal fluids. (English. Russian original) Zbl 1139.76010
Russ. Math. Surv. 62, No. 3, 409-451 (2007); translation from Usp. Mat. Nauk 62, No. 3, 5-46 (2007).
Summary: This article is a survey concerning the state-of-the-art mathematical theory of Euler equations for incompressible homogeneous ideal fluid. Emphasis is put on different types of emerging instability, and how they may be related to the description of turbulence.
MSC:
76B03 | Existence, uniqueness, and regularity theory for incompressible inviscid fluids |
76F06 | Transition to turbulence |
76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |
35Q30 | Navier-Stokes equations |