Generic Solvability of the Axisymmetric 3-D Euler Equations and the 2-D Boussinesq Equations

In this paper we first prove a new criterion of global solvability for smooth axisymmetric solutions of the 3-D Euler equations for a cylindrical type of domain, which can be whole R3. Then, using this result, we obtain generic solvability of the equations in the cylindrical domain which does not include the axis of symmetry. By a similar method we also obtain generic solvability of the 2-D Boussinesq system.