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.
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(Accepted June 10, 1998)
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Desjardins, B., Esteban, M. Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid. Arch Rational Mech Anal 146, 59–71 (1999). https://doi.org/10.1007/s002050050136
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DOI: https://doi.org/10.1007/s002050050136