Some properties on the surfaces of vector fields and its application to the Stokes and Navier–Stokes problems with mixed boundary conditions. (January 2015)

• Record Type: Journal Article
• Authors: Kim, Tujin; Cao, Daomin
• Is Part Of: Nonlinear analysis. Volume 113(2015)
• Page Start: 94
• Page End: 114
• Publication Date: 2015-01
• Subjects: 35Q35 -- 35A15 -- 76D03 -- 76D05 -- 76D07; Navier–Stokes equations -- Mixed boundary condition -- Stress boundary condition -- Pressure boundary condition -- Rotation boundary condition -- Existence -- Uniqueness; 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.2014.09.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we are concerned with the stationary and non-stationary Stokes and Navier–Stokes problems with mixed boundary conditions involving velocity, pressure, rotation, stress and normal derivative of velocity together. Relying on the relations among strain, rotation, normal derivative of velocity and shape of boundary surface, we get variational formulations of the Stokes and Navier–Stokes problems with the mixed boundary conditions. Also, we study existence and uniqueness of solutions to the problems.