Mathematical analysis of a one-dimensional model for an aging fluid

We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behaviour of the solutions

On flows of viscoelastic fluids of oldroyd type with wall slip

We consider the boundary-value problem for the steady isothermal flow of an incompressible viscoelastic liquid of Oldroyd type in a bounded domain with a Navier type slip boundary condition. We prove that under some restrictions on the material constants and the data, there exists a strong solution which is locally unique. The proof is based on a fixed point argument in which the boundary-value problem is decomposed into a transport equation and a Stokes system.http://link.springer.com/journal/21hb201