Fluid-Structure interactions with Navier- and full-slip boundary conditions

Abstract

We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works, the fluid is allowed to slip along the solid boundary; namely, the so called Navier-slip boundary conditions are considered. Such boundary conditions naturally involve the time-changing outer normal of the fluid domain. Hence, their dependence on the varying geometry is one degree higher than in the previously considered no-slip case, which makes it necessary to adjust the concept of weak coupled solutions. Two classes of test functions are introduced: test functions that are continuous over the fluid-solid domain, and fluid-only test functions with nonzero tangential component at the boundary. The weak equations are established until the point of contact, and moreover, compatibility with the strong formulation is shown.