On the motion of a small rigid body in a viscous compressible fluid

0573343 - MÚ 2024 RIV GB eng J - Journal Article
Feireisl, Eduard - Roy, A. - Zarnescu, A.
On the motion of a small rigid body in a viscous compressible fluid.
Communications in Partial Differential Equations. Roč. 48, č. 5 (2023), s. 794-818. ISSN 0360-5302. E-ISSN 1532-4133
R&D Projects: GA ČR(CZ) GA21-02411S
Institutional support: RVO:67985840
Keywords : body-fluid interaction problem * isentropic Navier-Stokes system * small rigid body
OECD category: Pure mathematics
Impact factor: 1.9, year: 2022
Method of publishing: Limited access
https://doi.org/10.1080/03605302.2023.2202733

We consider the motion of a small rigid object immersed in a viscous compressible fluid in the 3-dimensional Eucleidean space. Assuming the object is a ball of a small radius ε we show that the behavior of the fluid is not influenced by the object in the asymptotic limit (Formula presented.) The result holds for the isentropic pressure law (Formula presented.) for any (Formula presented.) under mild assumptions concerning the rigid body density. In particular, the latter may be bounded as soon as (Formula presented.) The proof uses a new method of construction of the test functions in the weak formulation of the problem, and, in particular, a new form of the so-called Bogovskii operator.
Permanent Link: https://hdl.handle.net/11104/0343806