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

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)


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