Strichartz Estimates for the Water-wave Problem with Surface Tension
نویسنده
چکیده
We study dispersive properties of one-dimensional surface waterwaves under surface tension, based on the formulation of the problem as a nonlinear dispersive equation coupled with a transport-type equation. We establish a dispersion estimate on time scales depending on the size of the frequencies. We infer that, if s is large enough, then a solution u of the dispersive equation satisfies local-in-time weighted Strichartz estimates with loss in the admissibility condition: ‖(1 + α)u‖Lp([0,T ])Ws,q(R) 6 C, 1 p + 1 q = 1 2 . The proof uses the frequency analysis for the linealized water-wave operator.
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