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Wellposedness of the tornado-hurricane equations

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  • 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 linearized system. An application of the contraction mapping principle then yields the existence of a unique local-in-time mild solution.
    Mathematics Subject Classification: Primary: 76D05, 76E07 ; Secondary: 35K20.

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