Generic solvability of the axisymmetric 3-D Euler equations and the 2-D Boussinesq equations (Q1303821)

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.