Unique solvability of the free-boundary Navier-Stokes equations with surface tension
| dc.creator | Coutand, Daniel | |
| dc.creator | Shkoller, Steve | |
| dc.date | 2002-12-09 | |
| dc.date | 2003-03-12 | |
| dc.date.accessioned | 2026-07-07T04:53:37Z | |
| dc.date.available | 2026-07-07T04:53:37Z | |
| dc.description | We prove the existence and uniqueness of solutions to the time-dependent incompressible Navier-Stokes equations with a free-boundary governed by surface tension. The solution is found using a topological fixed-point theorem for a nonlinear iteration scheme, requiring at each step, the solution of a model linear problem consisting of the time-dependent Stokes equation with linearized mean-curvature forcing on the boundary. We use energy methods to establish new types of spacetime inequalities that allow us to find a unique weak solution to this problem. We then prove regularity of the weak solution, and establish the a priori estimates required by the nonlinear iteration process. | |
| dc.description | 73 pages; typos corrected; minor details added | |
| dc.identifier | https://arxiv.org/abs/math/0212116 | |
| dc.identifier | http://arxiv.org/abs/math/0212116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65925 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q30;76D03;76B45 | |
| dc.title | Unique solvability of the free-boundary Navier-Stokes equations with surface tension | |
| dc.type | text |