Uniqueness results for weak solutions of two-dimensional fluid-solid systems
Analysis of PDEs
2024-12-30 v1
Abstract
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.
Cite
@article{arxiv.1203.2894,
title = {Uniqueness results for weak solutions of two-dimensional fluid-solid systems},
author = {Olivier Glass and Franck Sueur},
journal= {arXiv preprint arXiv:1203.2894},
year = {2024}
}