Generalized Navier–Stokes Equations with Non-Homogeneous Boundary Conditions

Autor:	Evgenii S. Baranovskii, Mikhail A. Artemov
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	generalized Navier–Stokes equations non-homogeneous Dirichlet boundary condition fractional Sobolev spaces trace operator divergence-free lifting operator strong solutions Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 6, Iss 7, p 373 (2022)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract6070373
Popis:	We study the generalized unsteady Navier–Stokes equations with a memory integral term under non-homogeneous Dirichlet boundary conditions. Using a suitable fractional Sobolev space for the boundary data, we introduce the concept of strong solutions. The global-in-time existence and uniqueness of a small-data strong solution is proved. For the proof of this result, we propose a new approach. Our approach is based on the operator treatment of the problem with the consequent application of a theorem on the local unique solvability of an operator equation involving an isomorphism between Banach spaces with continuously Fréchet differentiable perturbations.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/07704878c2ca430ab5df321d3d987228 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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