TY - JOUR
T1 - Local smoothing effects for the water-wave problem with surface tension
AU - Christianson, Hans
AU - Hur, Vera Mikyoung
AU - Staffilani, Gigliola
PY - 2009/2
Y1 - 2009/2
N2 - 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).
AB - 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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U2 - 10.1016/j.crma.2008.12.010
DO - 10.1016/j.crma.2008.12.010
M3 - Article
AN - SCOPUS:60449104603
SN - 1631-073X
VL - 347
SP - 159
EP - 162
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 3-4
ER -