Dh. Chae et Oy. Imanuvilov, Generic solvability of the axisymmetric 3-D Euler equations and the 2-D Boussinesq equations, J DIFF EQUA, 156(1), 1999, pp. 1-17
In this paper we first prove a new criterion of global solvability for smoo
th axisymmetric solutions of the 3-D Euler equations for a cylindrical type
of domain, which can be whole R-3. Then, using this result, we obtain gene
ric solvability of the equations in the cylindrical domain which does not i
nclude the axis of symmetry. By a similar method we also obtain generic sol
vability of the 2-D Boussinesq system. (C) 1999 Academic Press.