Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid |
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| Authors: | B Desjardins M J Esteban |
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| Institution: | (1) Département de Mathématiques et d'Informatique, Ecole Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France e‐mail: desjardi@dmi.ens.fr, FR;(2) CEREMADE (UMR 7534), Université Paris‐Dauphine, Place de Lattre de Tassigny, 75775 Paris Cedex 16, e‐mail: esteban@ceremade.dauphine.fr, FR |
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| Abstract: | . We study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of with Dirichlet boundary conditions. By introducing an appropriate weak formulation for the complete problem, we prove existence
of solutions for initial velocities in . 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.
(Accepted June 10, 1998) |
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| Keywords: | |
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