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Maria Eugenia MARTINEZ

The soliton problem for the Zakharov water waves problem with slowly varying bottom.

Zakharov water waves arises as a free surface model for an irrotational and incompressible fluid under the influence of gravity. Such fluid is considered in a domain with rigid bottom (described as ha(x)) and a free surface. When considering the pressure over the surface, Amick-Kirchgässner proved the existence of solitary waves Qc (solutions that maintain its shape as they travel in time) of speed c for the flat-bottom case (a=1). In this talk, we are interested in the analysis of the behavior of the solitary wave solution of the flat-bottom problem when the bottom actually presents a (slight) change at some point. We construct a solution to the Zakharov water waves system with non-flat bottom that is time assympotic (as time t tends to - infinity) to the Amick-Kirchgässner soliton Q_c

evenements/abstract_martinez.txt · Last modified: 2022/02/13 20:33 by Pierre Gilles Lemarié

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