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 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.