Strichartz estimates for the water-wave problem with surface tension

Hans Christianson, Vera Mikyoung Hur, Gigliola Staffilani

Research output: Contribution to journalArticlepeer-review

Abstract

Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales depending on the size of the frequencies. We infer that a solution u of the dispersive equation we introduce satisfies local-in-time Strichartz estimates with loss in derivative: where C depends on T and on the norms of the Hs-norm of the initial data. The proof uses the frequency analysis and semiclassical Strichartz estimates for the linealized water-wave operator.

Original languageEnglish (US)
Pages (from-to)2195-2252
Number of pages58
JournalCommunications in Partial Differential Equations
Volume35
Issue number12
DOIs
StatePublished - Dec 2010
Externally publishedYes

Keywords

  • Nonlinear dispersive elements
  • Strichartz estimates
  • Water waves

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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