Gain of regularity for water waves with surface tension
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.
Keywords
Cite
@article{arxiv.1210.0162,
title = {Gain of regularity for water waves with surface tension},
author = {Vera Mikyoung Hur},
journal= {arXiv preprint arXiv:1210.0162},
year = {2012}
}