Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9500077 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2005 | 29 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Ben Schweizer,