A uniqueness result for 3D incompressible fluid-rigid body interaction problem

0534794 - MÚ 2022 RIV CH eng J - Journal Article
Muha, B. - Nečasová, Šárka - Radoševič, Ana
A uniqueness result for 3D incompressible fluid-rigid body interaction problem.
Journal of Mathematical Fluid Mechanics. Roč. 23, č. 1 (2021), č. článku 1. ISSN 1422-6928. E-ISSN 1422-6952
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : fluid flow * 3D incompressible fluid-rigid body interaction
OECD category: Pure mathematics
Impact factor: 1.907, year: 2021
Method of publishing: Limited access
https://doi.org/10.1007/s00021-020-00542-2

We study a 3D nonlinear moving boundary fluid-structure interaction problem describing the interaction of the fluid flow with a rigid body. The fluid flow is governed by 3D incompressible Navier-Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations called Euler equations for the rigid body. The equations are fully coupled via dynamical and kinematic coupling conditions. We consider two different kinds of kinematic coupling conditions: no-slip and slip. In both cases we prove a generalization of the well-known weak-strong uniqueness result for the Navier-Stokes equations to the fluid-rigid body system. More precisely, we prove that weak solutions that additionally satisfy the Prodi-Serrin Lr−Ls condition are unique in the class of Leray-Hopf weak solutions.
Permanent Link: http://hdl.handle.net/11104/0312962