Strichartz Estimates for the Water-Wave Problem with Surface Tension
Author(s)Christianson, Hans; Hur, Vera Mikyoung; Staffilani, Gigliola
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications in Partial Differential Equations
Taylor & Francis Group
Christianson, Hans, Vera Mikyoung Hur, and Gigliola Staffilani. “Strichartz Estimates for the Water-Wave Problem with Surface Tension.” Communications in Partial Differential Equations 35.12 (2010): 2195–2252. Web.
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