Abstract:

In this paper the weak solvability of one Voigt--$\alpha$ model with infinite memory is investigated. The topological approximation method for studying hydrodynamic problems is used to prove the weak solvability of this model. Also the theory of regular Lagrangian flow is used in the study of weak solvability. The existence of a weak solution of the problem is proved in the paper. Also the convergence of solutions of the alpha--model to solutions of the original model as the parameter $\alpha$ tends to zero is established.