About this scholarly article

On the Regularity of Weak Solutions to the Fluid-rigid Body Interaction Problem by Muha, Boris; Nečasová, Šárka; Radošević, Ana is a scholarly article available to read on EtoBox.

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 $C^{\infty}$ if additionally we assume that the rigid body acceleration is bounded almost anywhere in time variable.

Author

Muha, Boris; Nečasová, Šárka; Radošević, Ana

Published

2022

Language

EN