Weak-strong uniqueness for the compressible fluid-rigid body interaction

0521522 - MÚ 2021 RIV US eng J - Journal Article
Kreml, Ondřej - Nečasová, Šárka - Piasecki, T.
Weak-strong uniqueness for the compressible fluid-rigid body interaction.
Journal of Differential Equations. Roč. 268, č. 8 (2020), s. 4756-4785. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : fluid-structure interaction * fluid * incompressible fluid
OECD category: Pure mathematics
Impact factor: 2.430, year: 2020
Method of publishing: Limited access
https://doi.org/10.1016/j.jde.2019.10.038

In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position and velocity of the rigid body in the fluid are unknown and the motion of the rigid body is driven by the normal stress forces of the fluid acting on the boundary of the body. We prove that the strong solution, which is known to exist under certain smallness assumptions, is unique in the class of weak solutions to the problem. The proof relies on a correct definition of the relative energy, to use this tool we then have to introduce a change of coordinates to transform the strong solution to the domain of the weak solution in order to use it as a test function in the relative energy inequality. Estimating all arising terms we prove that the weak solution has to coincide with the transformed strong solution and finally that the transformation has to be in fact an identity.
Permanent Link: http://hdl.handle.net/11104/0306120