Asymptotic analysis of the non-steady Navier–Stokes equations in a tube structure. II. General case. (September 2015)

• Record Type: Journal Article
• Authors: Panasenko, Grigory; Pileckas, Konstantin
• Is Part Of: Nonlinear analysis. Volume 125(2015)
• Page Start: 582
• Page End: 607
• Publication Date: 2015-09
• Subjects: Navier–Stokes equations -- Thin structures -- Asymptotics -- Boundary layers; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.05.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The non-steady Navier–Stokes equations with Dirichlet boundary conditions are considered in thin tube structures. These domains are connected finite unions of thin finite cylinders (in the 2 D case respectively thin rectangles). The complete asymptotic expansion of the solution is constructed. It contains a regular part and three types of the boundary layer correctors: "in-space", "in-time" and "in-space-and-in-time". The estimates for the difference of the exact solution and its J th asymptotic approximation are proved.