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

2022/08/16 by Eduard Feireisl, Arnab Roy, Feireisl, Eduard +3 · 1 citation
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2208.07933

openalex publication_date 2022/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

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 ε → 0. The result holds for the isentropic pressure law p(\varrho) = a \varrho^γ for any γ> (3)/(2) under mild assumptions concerning the rigid body density. In particular, the latter may be bounded as soon as γ> 3. 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.

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