Two dimensional solitary waves in shear flows
In this paper we study existence and asymptotic behavior of solitary-wave solutions for the generalized Shrira equation, a two-dimensional model appearing in shear flows. The method used to show the existence of such special solutions is based on the mountain pass theorem. One of the main difficulties consists in showing the compact embedding of the energy space in the Lebesgue spaces; this is dealt with interpolation theory. Regularity and decay properties of the solitary waves are also established.
Mathematics Subject Classification35Q35 35B65 35A15 35B40
The second author is partially supported by CNPq-Brazil and FAPESP-Brazil. The authors would like to thank F.H. Soriano for the helpful discussion concerning the construction of the extension operator and the referee for the careful reading and suggestions which improve the presentation of the paper.
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