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- W4298082604 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." @default.
- W4298082604 created "2022-10-01" @default.
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- W4298082604 date "2012-09-29" @default.
- W4298082604 modified "2023-09-29" @default.
- W4298082604 title "Gain of regularity for water waves with surface tension" @default.
- W4298082604 doi "https://doi.org/10.48550/arxiv.1210.0162" @default.
- W4298082604 hasPublicationYear "2012" @default.
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