Contributors: Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore; Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX); Inria Nancy - Grand Est; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); Institut Élie Cartan de Lorraine (IECL); Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS); The first author is partially supported by INSPIRE faculty fellowship (IFA18-MA128) and by Department of Atomic Energy, Government of India, under Project no. 12-R & D-TFR-5.01-0520.; The second author is partially supported by the French National Research Agency, Project TRECOS, ANR-20-CE40-0009; ANR-20-CE40-0009,TRECOS,Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux(2020)
Abstract: International audience ; In this article, we study the weak uniqueness and the regularity of the weak solutions of a fluid-structure interaction system. More precisely, we consider the motion of a rigid ball in a viscous incompressible fluid and we assume that the fluid-rigid body system fills the entire space $\mathbb{R}^3$. We prove that the corresponding weak solutions that additionally satisfy a classical Prodi-Serrin condition, including a critical one, are unique. We also show that the weak solutions are regular under the Prodi-Serrin conditions, with a smallness condition in the critical case.
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