On the vanishing rigid body problem in a viscous compressible fluid

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 sys...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2023-02, Vol.345, p.45-77
Main Authors: Bravin, Marco, Nečasová, Šárka
Format: Article
Language:English
Subjects:
Asymptotic limit
Compressible Navier-Stokes
Fluid-structure interaction
PDEs
Rigid body
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 γ≥6.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.11.023