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

Olivier Glass (1) , Franck Sueur (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LJLL - Laboratoire Jacques-Louis Lions

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.

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Glass, Franck Sueur. Uniqueness results for weak solutions of two-dimensional fluid-solid systems. Archive for Rational Mechanics and Analysis, 2015, 218 (2), pp.907-944. ⟨hal-00678687⟩