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Two dimensional solitary waves in shear flows. (English) Zbl 1395.35165

Summary: 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
35A15 Variational methods applied to PDEs
35B40 Asymptotic behavior of solutions to PDEs
35C08 Soliton solutions
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