Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501713 | Journal of Differential Equations | 2005 | 31 Pages |
Abstract
In this paper, we consider the Hele-Shaw problem in a 2-dimensional fluid domain Ωt which is constrained to a half-plane. The boundary of Ωt consist of two components: Î0t which lies on the boundary of the half-plane, and Ît which lies inside the half-plane. On Ît we impose the classical boundary conditions with surface tension, and on Î0t we prescribe the normal derivative of the fluid pressure. At the point where Î0t and Ît meet, there is an abrupt change in the boundary condition giving rise to a singularity in the fluid pressure. We prove that the problem has a unique solution with smooth free boundary Ît for some small time interval.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Borys V. Bazaliy, Avner Friedman,