论文信息 - Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid

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.

Benoît Desjardins | Maria J. Esteban | B. Desjardins | M. Esteban

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