On the strong solutions of a regularized model of a nonlinear visco-elastic medium

Abstract

We consider the initial boundary-value problem for the system of equations describing the motion of a nonlinear visco-elastic medium with memory along the trajectories of the velocity field; the system in question is a generalization of the system of Navier-Stokes equations. We establish existence and uniqueness theorems for strong solutions containing higher derivatives that are square-integrable in the plane case.