Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid
Abstract
. We study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of $\R^d$ $(d=2$ or $3)$ with Dirichlet boundary conditions. By introducing an appropriate weak formulation for the complete problem, we prove existence of solutions for initial velocities in $H^1_0(\Omega)$. In the absence of collisions, solutions exist for all time in dimension 2, whereas in dimension 3 the lifespan of solutions is infinite only for small enough data.
- Publication:
-
Archive for Rational Mechanics and Analysis
- Pub Date:
- April 1999
- DOI:
- 10.1007/s002050050136
- Bibcode:
- 1999ArRMA.146...59D
- Keywords:
-
- Boundary Condition;
- Weak Solution;
- Rigid Body;
- Finite Number;
- Bounded Domain