Strong Solutions of the Incompressible Navier–Stokes–Voigt Model

Evgenii S. Baranovskii
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Evgenii S. Baranovskii: Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, Russia

Mathematics, 2020, vol. 8, issue 2, 1-16

Abstract: This paper deals with an initial-boundary value problem for the Navier–Stokes–Voigt equations describing unsteady flows of an incompressible non-Newtonian fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Faedo–Galerkin method with a special basis of eigenfunctions of the Stokes operator, we construct a global-in-time strong solution, which is unique in both two-dimensional and three-dimensional domains. We also study the long-time asymptotic behavior of the velocity field under the assumption that the external forces field is conservative.

Keywords: Navier–Stokes–Voigt equations; viscoelastic models; non-Newtonian fluid; strong solutions; existence and uniqueness theorem; Faedo–Galerkin approximations; Stokes operator; long-time behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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