Fluid-Viscoelastic Interaction

We consider the viscoelastic Navier-Stokes-Biot model coupling the 3D incompressible Navier-Stokes equations with the Biot model describing the motion of poroviscoelastic material. The coupling between fluid and porous media is described by the Beavers-Joseph-Saffman interface condition. We will show that the coupled system admits a unique, global strong solution for small data. Furthermore, local existence for arbitrary data and a Serrin-type blow-up criterium will be discussed.