Galerkin approximations and the solution of the problem of two-dimensional unsteady motion of a viscous incompressible two-component fluid Full article
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Computational Mathematics and Modeling
ISSN: 1046-283X |
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| Output data | Year: 2026, Pages: 1-12 Pages count : 12 DOI: 10.1007/s10598-026-09740-5 | ||
| Tags | Dynamics of the mixture, viscosity matrix, initial-boundary value problem, Galerkin approximation, weak solution | ||
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Abstract:
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.
Cite:
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
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
Dates:
| Submitted: | Jun 25, 2026 |
| Accepted: | Aug 3, 2026 |
| Published online: | Aug 17, 2026 |
Identifiers:
| ≡ Scopus: | 2-s2.0-105047571090 |
| ≡ OpenAlex: | W7203604843 |