Existence results for the flow of a nonhomogeneous visco-elastic fluid

Abstract- In this paper, we are concerned with a physical system that contains uid and viscohyperelastic particles. Following the method introduced in [2], we pose the full system of equations modelling the motion of the two-phase system uid and solid particles. It is brie y shown that the system we are going to study is a type of non-Newtonian uid, namely, a uid with memory like an Oldroyd model. The nonlinearity of elastic stress tensor and the evolution equation of the deformation are serious obstacles to the existence of a weak solution. In this paper, under regularity of the data, we prove some local and, for small data, global (in time) existence results.