Viscoelastic Fluid Model with Nonhomogeneous Boundary Conditions

Abstract

We deal with a viscoelastic fluid model in a rectangle domain with nontrivial velocity at the inflow and outflow area and slip boundary condition at the rest of the boundary. For this model we investigate the existence of local in time solutions. Then we present 2D simulations and we discuss the possibility of the derivation of 1D model by limit passage with the height of the rectangle to zero. Moreover, we present few 1D models that we support by simulations.