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Pré-Publication, Document De Travail Année : 2015

A dispersive estimate for the linearized Water-Waves equations in finite depth

Résumé

We prove a dispersive estimate for the solutions of the linearized Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a decay with respect to time t of order 1/3 for solutions with initial data in weighted Sobolev spaces. We also give variants to this result with different decays for a more convenient use of the dispersive estimate. We then give an existence result for the full Water-Waves equations in weighted spaces for practical uses of the proven dispersive estimates.
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Dates et versions

hal-01238616 , version 1 (06-12-2015)

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Benoît Mésognon-Gireau. A dispersive estimate for the linearized Water-Waves equations in finite depth. 2015. ⟨hal-01238616⟩
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