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Uniqueness results for weak solutions of two-dimensional fluid-solid systems

Sueur, Franck; Glass, Olivier (2015), Uniqueness results for weak solutions of two-dimensional fluid-solid systems, Archive for Rational Mechanics and Analysis, 218, 2, p. 907-944. 10.1007/s00205-015-0876-8

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00678687
Date
2015
Journal name
Archive for Rational Mechanics and Analysis
Volume
218
Number
2
Publisher
Springer
Pages
907-944
Publication identifier
Metadata
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Author(s)
Sueur, Franck

Glass, Olivier
Abstract (EN)
In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible fluid in a bounded domain of the plane. The first system corresponds to an inviscid fluid driven by the Euler equation whereas the other one corresponds to a viscous fluid driven by the Navier-Stokes system. In both cases we investigate the uniqueness of weak solutions, "à la Yudovich" for the Euler case, "à la Leray" for the Navier-Stokes case, as long as no collision occurs.
Subjects / Keywords
fluid-solid systems; Uniqueness of solutions; weak solutions