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

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

2012-03-13

arxiv.org/abs/1203.2894v1

Mathematics

Analysis of PDEs

Scientific paper

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, "\`a la Yudovich" for the Euler case, "\`a la Leray" for the Navier-Stokes case, as long as no collision occurs.

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