|Title:||On the three-dimensional Euler equations with a free boundary subject to surface tension|
|Abstract:||We study an incompressible ideal fluid with a free surface that is subject to surface tension; it is not assumed that the fluid is irrotational. We derive a priori estimates for smooth solutions and prove a short-time existence result. The bounds are obtained by combining estimates of energy type with estimates of vorticity type and rely on a careful study of the regularity properties of the pressure function. An adequate artificial coordinate system is used instead of the standard Lagrangian coordinates. Under an assumption on the vorticity, a solution to the Euler equations is obtained as a vanishing viscosity limit of solutions to appropriate Navier–Stokes systems.|
|Citation:||Ben Schweizer, On the three-dimensional Euler equations with a free boundary subject to surface tension, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 22, Issue 6, November-December 2005, Pages 753-781, ISSN 0294-1449, DOI: 10.1016/j.anihpc.2004.11.001.|
|Appears in Collections:||Schweizer, Ben Prof. Dr.|
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