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Uniqueness and regularity of weak solutions of a fluid-rigid body interaction system under the Prodi-Serrin condition

  • *Corresponding author: Takéo Takahashi

    *Corresponding author: Takéo Takahashi

The first author is partially supported by INSPIRE faculty fellowship (IFA18-MA128) and by Department of Atomic Energy, Government of India, under Project no. 12-R & D-TFR-5.01-0520. The second author is partially supported by the French National Research Agency, Project TRECOS, ANR-20-CE40-0009

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  • In this article, we study the weak uniqueness and the regularity of the weak solutions of a fluid-structure interaction system. More precisely, we consider the motion of a rigid ball in a viscous incompressible fluid and we assume that the fluid-rigid body system fills the entire space $ \mathbb{R}^{3}. $ We prove that the corresponding weak solutions that additionally satisfy a classical Prodi-Serrin condition, including a critical one, are unique. We also show that the weak solutions are regular under the Prodi-Serrin conditions, with a smallness condition in the critical case.

    Mathematics Subject Classification: 35Q35, 76D03, 76D05, 74F10.

    Citation:

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