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arXiv · 2208.07933

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

Eduard Feireisl·Arnab Roy·Arghir Zarnescu
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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 $\varepsilon$ we show that the behavior of the fluid is not influenced by the object in the asymptotic limit $\varepsilon \to 0$. The result holds for the isentropic pressure law $p(\varrho) = a \varrho^\gamma$ for any $\gamma > \frac{3}{2}$ under mild assumptions concerning the rigid body density. In particular, the latter may be bounded as soon as $\gamma > 3$. 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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Eduard Feireisl, Arnab Roy, Arghir Zarnescu. 2022-08-16. On the motion of a small rigid body in a viscous compressible fluid. https://arxiv.org/abs/2208.07933

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