On Solvability of an Initial-Boundary Value Problem for a Viscoelasticity Model with Fractional Derivatives

We establish the existence and uniqueness (the latter only in the plane case) of a weak solution to an initial-boundary value problem for the system of the equations of motion of a viscoelastic fluid, namely, for the anti-Zener model whose constitutive law contains fractional derivatives. We use the approximation of this problem by a sequence of regularized Navier-Stokes systems and passage to the limit.