A dispersive estimate for the linearized Water-Waves equations in finite depth
Analysis of PDEs
2015-12-09 v1
Abstract
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.
Cite
@article{arxiv.1512.02423,
title = {A dispersive estimate for the linearized Water-Waves equations in finite depth},
author = {Benoît Mésognon-Gireau},
journal= {arXiv preprint arXiv:1512.02423},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1407.4369