English

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.

Keywords

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

R2 v1 2026-06-22T12:04:06.677Z