Galerkin approximations and the solution of the problem of two-dimensional unsteady motion of a viscous incompressible two-component fluid

Galerkin approximations and the solution of the problem of two-dimensional unsteady motion of a viscous incompressible two-component fluid Научная публикация

Журнал

Computational Mathematics and Modeling
ISSN: 1046-283X

Вых. Данные

Год: 2026, Страницы: 1-12 Страниц : 12 DOI: 10.1007/s10598-026-09740-5

Ключевые слова

Dynamics of the mixture, viscosity matrix, initial-boundary value problem, Galerkin approximation, weak solution

Авторы

Prokudin D.A. ¹

Организации

1	Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences

We consider equations describing two-dimensional unsteady motion of a binary mixture of viscous incompressible fluids. A theorem on the existence and uniqueness of a weak solution to the initial-boundary value problem corresponding to the flow of the mixture in a bounded domain is proved. To prove the existence of a solution, we consider an approximation problem for the Galerkin approximations, establish its solvability and a priori estimates that are independent of the approximation parameter. Then a limit passage with respect to the approximation parameter is performed, and it is shown that the Galerkin approximations converge weakly to a solution of the original problem. The uniqueness of the solution is established using Gronwall’s inequality.

Prokudin D.A.
Galerkin approximations and the solution of the problem of two-dimensional unsteady motion of a viscous incompressible two-component fluid
Computational Mathematics and Modeling. 2026. P.1-12. DOI: 10.1007/s10598-026-09740-5 Scopus OpenAlex

Поступила в редакцию:	25 июн. 2026 г.
Принята к публикации:	3 авг. 2026 г.
Опубликована online:	17 авг. 2026 г.

≡ Scopus:	2-s2.0-105047571090
≡ OpenAlex:	W7203604843