We prove local-in-time existence of a unique mild
solution for the tornado-hurricane
equations in a Hilbert space setting.
The wellposedness is shown simultaneously
in a halfspace, a layer, and a cylinder and for various
types of boundary conditions which admit discontinuities
at the edges of the cylinder. By an approach based on
symmetric forms we first prove maximal regularity for a
An application of the
contraction mapping principle then yields the
existence of a unique local-in-time mild solution.