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April  2010, 26(2): 649-664. doi: 10.3934/dcds.2010.26.649

Wellposedness of the tornado-hurricane equations

Jürgen Saal 1,

1. 

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

Received  December 2008 Revised  June 2009 Published  October 2009

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: cyclones., Weakly compressible Navier-Stokes equations, wellposedness.
Mathematics Subject Classification: Primary: 76D05, 76E07 ; Secondary: 35K2.
Citation: Jürgen Saal. Wellposedness of the tornado-hurricane equations. Discrete & Continuous Dynamical Systems, 2010, 26 (2) : 649-664. doi: 10.3934/dcds.2010.26.649
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