Fluid-Rigid Structure Interaction System with Coulomb's Law

Abstract

We propose a new model in a fluid-rigid structure system composed by a rigid body and a viscous incompressible fluid using a boundary condition based on Coulomb's law. This boundary condition allows the fluid to slip on the boundary if the tangential component of the stress is too large. In the opposite case, we recover the standard Dirichlet boundary condition. The governing equations are the Navier--Stokes system for the fluid and the Newton laws for the body. The corresponding coupled system can be written as a variational inequality. We prove that there exists a weak solution of this system.