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

0534794 - MÚ 2022 RIV CH eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GA19-04243S
Institucionální podpora: RVO:67985840
Klíčová slova: fluid flow * 3D incompressible fluid-rigid body interaction
Obor OECD: Pure mathematics
Impakt faktor: 1.907, rok: 2021
Způsob publikování: Omezený přístup
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.
Trvalý link: http://hdl.handle.net/11104/0312962