Generic solvability of the axisymmetric 3-D Euler equations and the 2-D Boussinesq equations. (English) Zbl 0939.35149

Chae, Dongho; Imanuvilov, Oleg Yu.

J. Differ. Equations 156, No. 1, 1-17 (1999).

Using a new criterion for finite-time blow-up of a smooth axisymmetric solutions to incompressible Euler equations, the authors prove global existence of smooth axisymmetric solutions in a domain of cylindrical type, which can be the whole \(\mathbb{R}^3\). Then using this results, the authors establish the solvability of Euler equations in cylindrical domains which do not contain the axis of symmetry. Similar results are also proved for two-dimensional Boussinesq system.

Reviewer: O.Titow (Berlin)

MSC:

35Q35	PDEs in connection with fluid mechanics
76B03	Existence, uniqueness, and regularity theory for incompressible inviscid fluids

Keywords:

finite-time blow-up; smooth axisymmetric solutions; incompressible Euler equations; global existence; cylindrical domains; two-dimensional Boussinesq system

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