Strichartz Estimates for the Water-Wave Problem with Surface Tension

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 H s -norm of the initial data. The proof uses the frequency analysis and semiclassical Strichartz estimates for the linealized water-wave operator.

Locations

• Communications in Partial Differential Equations - View
• arXiv (Cornell University) - View - PDF
• DSpace@MIT (Massachusetts Institute of Technology) - View - PDF