Weak solvability of fractional Voigt model of viscoelasticity

Abstract

In the present paper we establish the existence of weak solutions to one fractional Voigt type model of viscoelastic fluid. This model takes into account a memory along the motion trajectories. The investigation is based on the theory of regular Lagrangean flows, approximation of the problem under consideration by a sequence of regularized Navier-Stokes systems and the following passage to the limit.