Wellposedness of the tornado-hurricane equations

Jürgen Saal

doi:10.3934/dcds.2010.26.649

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2010, Volume 26, Issue 2: 649-664. Doi: 10.3934/dcds.2010.26.649

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Wellposedness of the tornado-hurricane equations

Jürgen Saal^1,

1.
University of Konstanz, Department of Mathematics and Statistics, Box D 187, 78457 Konstanz

Received: November 30, 2008

Revised: May 31, 2009

Published: June 2010

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Abstract

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.

Keywords:

Weakly compressible Navier-Stokes equations,
wellposedness,
cyclones.

Mathematics Subject Classification: Primary: 76D05, 76E07 ; Secondary: 35K20.

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