On the vanishing rigid body problem in a viscous compressible fluid

0564462 - MÚ 2024 RIV US eng J - Journal Article
Bravin, M. - Nečasová, Šárka
On the vanishing rigid body problem in a viscous compressible fluid.
Journal of Differential Equations. Roč. 345, February 5 (2023), s. 45-77. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : PDEs * fluid-structure interaction * asymptotic limit * compressible Navier-Stokes * rigid body
OECD category: Pure mathematics
Impact factor: 2.4, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.jde.2022.11.023

In this paper we study the interaction of a small rigid body in a viscous compressible fluid. The system occupies a bounded three dimensional domain. The object it allowed to freely move and its dynamics follows the Newton's laws. We show that as the size of the object converges to zero the system fluid plus rigid body converges to the compressible Navier-Stokes system under some mild lower bound on the mass and the inertia momentum. It is a first result of homogenization in the case of fluid-structure interaction in the compressible situation. As a corollary we slightly improved the result on the influence of a vanishing obstacle in a compressible fluid for gama >=6.
Permanent Link: https://hdl.handle.net/11104/0336119