Strichartz Estimates for the Water-Wave Problem with Surface Tension
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Staffilani_Strichartz Estimates.pdf
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Author(s)
Christianson, Hans
Hur, Vera Mikyoung
Staffilani, Gigliola
Date Issued
October 2010
Journal
Communications in Partial Differential Equations
Publisher
Taylor & Francis Group
Citation
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.
Version
Author's final manuscript
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[superscript s]-norm of the initial data. The proof uses the frequency analysis and semiclassical Strichartz estimates for the linealized water-wave operator.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1080/03605301003758351
