Abstract
This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole ℝ3. The fluid is modelled by the incompressible nonhomogeneous Navier-Stokes system with a nonnegative density. The motion of the rigid body is described by the balance of linear and angular momentum. We consider the case where slip is allowed at the fluid-solid interface through Navier condition and prove the global existence of a weak solution.
Highlights
Fluid-structure interaction (FSI) systems are systems which include a fluid and a solid component
In this article we consider the case of non-steady self-propelled motion in the case of a nonhomogeneous fluid with Navier boundary conditions
Following [16, 28, 30], we apply a global change of variables that transforms the system in such a way that it is formulated in a frame which is attached to the rigid body
Summary
Fluid-structure interaction (FSI) systems are systems which include a fluid and a solid component. In this article we consider the case of non-steady self-propelled motion in the case of a nonhomogeneous fluid (non-constant density) with Navier boundary conditions. In order to prove existence of a weak solution we first establish such an existence on a bounded domain BR = {y ∈ R3 |y| < R} by extending work of [35] to the setting with a self-propelled rigid body. The novelties of our paper are as follows: (1) we include self-propelled motion of the rigid body, (2) we allow for nonnegative and nonhomogeneous densities and (3) replace the no-slip condition at the interface of the solid and the fluid by the Navier slip condition. In the appendix we present a derivation of the weak formulation of the problem
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