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- Title
On the regularity of weak solutions to the fluid–rigid body interaction problem.
- Authors
Muha, Boris; Nečasová, Šárka; Radošević, Ana
- Abstract
We study a 3D fluid–rigid body interaction problem. The fluid flow is governed by 3D incompressible Navier–Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations describing conservation of linear and angular momentum. Our aim is to prove that any weak solution satisfying certain regularity conditions is smooth. This is a generalization of the classical result for the 3D incompressible Navier–Stokes equations, which says that a weak solution that additionally satisfy Prodi–Serrin L r - L s condition is smooth. We show that in the case of fluid–rigid body the Prodi–Serrin conditions imply W 2 , p and W 1 , p regularity for the fluid velocity and fluid pressure, respectively. Moreover, we show that solutions are C ∞ if additionally we assume that the rigid body acceleration is bounded almost anywhere in time variable.
- Subjects
FLUID-structure interaction; RIGID bodies; ORDINARY differential equations; ANGULAR momentum (Mechanics); NAVIER-Stokes equations; LINEAR momentum; FLUID pressure
- Publication
Mathematische Annalen, 2024, Vol 389, Issue 2, p1007
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-023-02664-0