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Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid

Desjardins, Benoît; Esteban, Maria J. (1999), Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid, Archive for Rational Mechanics and Analysis, 146, 1, p. 59-71. http://dx.doi.org/10.1007/s002050050136

Type
Article accepté pour publication ou publié
Date
1999
Journal name
Archive for Rational Mechanics and Analysis
Volume
146
Number
1
Publisher
Springer
Pages
59-71
Publication identifier
Metadata
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Author(s)
Desjardins, Benoît
Esteban, Maria J. cc
Abstract (EN)
We study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of Rd (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 H10 (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.
Subjects / Keywords
weak formulation; rigid bodies; viscous incompressible fluid; Dirichlet boundary conditions