Gain of regularity for water waves with surface tension

Vera Mikyoung Hur

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arXiv · 1210.0162

Gain of regularity for water waves with surface tension

Vera Mikyoung Hur

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Abstract

Regularizing effects of surface tension are studied for interfacial waves between a two-dimensional, infinitely-deep and irrotational flow of water and vacuum. The water wave problem under the influence of surface tension is formulated as a system of second-order in time nonlinear dispersive equations. The main result states that if the curvature of the initial fluid surface is in the Sobolev space of order k+7/2 and if its derivatives decay faster than a polynomial of degree k+1 does then the curvature of the fluid surface corresponding to the solution of the problem instantaneously gains k/2 derivatives of smoothness compared to the initial state. The proof uses energy estimates under invariant vector fields of the associated linear operator.

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Vera Mikyoung Hur. 2012-09-30. Gain of regularity for water waves with surface tension. https://arxiv.org/abs/1210.0162

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