Strichartz Estimates for the Water-Wave Problem with Surface Tension

• Main Authors: Christianson, Hans (Contributor), Hur, Vera Mikyoung (Contributor), Staffilani, Gigliola (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Taylor & Francis Group, 2012-07-17T18:16:50Z.
• Subjects: Article
• Online Access: Get fulltext

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[superscript s]-norm of the initial data. The proof uses the frequency analysis and semiclassical Strichartz estimates for the linealized water-wave operator.
National Science Foundation (U.S.) (Postdoctoral Fellowship)
National Science Foundation (U.S.) (NSF grants DMS-0707647)
National Science Foundation (U.S.) (NSF grant DMS-1002854)
National Science Foundation (U.S.) (NSF grant DMS-0602678)