The water-wave problem with a one-dimensional free surface of infinite depth is considered, based on the formulation as a second-order nonlinear dispersive equation. The local smoothing effects are established under the influence of surface tension, stating that on average in time solutions acquire locally 1/4 derivative of smoothness as compared to the initial state. The analysis combines energy methods with techniques of Fourier integral operators. To cite this article: H. Christianson et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).
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