A study of the solvability of the Bingham alpha model

A. V. Zvyagin, N. V. Tolstoy

Voronezh State University, Voronezh, Russia

Abstract: This article studies the solvability of the initial-boundary value problem for the alpha model of a Bingham-type viscoplastic fluid with periodic conditions on the spatial variables. Using an approximation-topological approach, we prove the existence of weak solutions to the alpha model under study and establish the convergence of the alpha model solutions to the solutions of the original model as the alpha parameter tends to zero.

Keywords: Bingham alpha model, viscoplastic fluid, initial-boundary value problem, approximation-topological approach, existence of weak solutions, convergence of solutions.

UDC: 517.957

DOI: 10.22363/2413-3639-2025-71-4-604-625