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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2024

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

Résumé

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.
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Dates et versions

hal-04075090 , version 1 (19-04-2023)

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Debayan Maity, Takéo Takahashi. Uniqueness and regularity of weak solutions of a fluid-rigid body interaction system under the Prodi-Serrin condition. Discrete and Continuous Dynamical Systems - Series A, 2024, 44 (3), pp.718-742. ⟨10.3934/dcds.2023123⟩. ⟨hal-04075090⟩
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