Weak Solvability of the Initial Boundary Value Problem for the Voigt Model with a Smoothed Jaumann Time Derivative Taking into Account the Memory of Fluid Motion

The paper establishes the solvability in the weak sense of the initial-boundary value problem for the Voigt model with a smoothed Jaumann derivative with respect to time, taking into account the memory of fluid motion. The proof is carried out on the base of the approximation-topological approach to the study of fluid dynamics problems. Namely, some approximation problem is considered and its solvability is established using the Leray–Schauder degree theory. Then, based on a priori estimates, the passage to the limit is carried out and it is shown that the solutions of the approximation problem weakly converge to the solution of the original problem as the approximation parameter tends to zero.