On weak solvability of fractional models of viscoelastic high order fluid

Abstract

In this paper, we establish the existence of a weak solution to the initial boundary value problem for the motion equations of viscoelastic incompressible fluid with constitutive law containing high-order fractional derivatives and with memory along the trajectories of the velocity field. The proof is by approximation of the original problem by a sequence of regularized problems followed by a passage to the limit based on appropriate a priori estimates. Methods of the theory of fractional derivatives calculus and the theory of regular Lagrangian flows (generalization of the classical solution of ODE systems) are used.