Boundary partial regularity for steady flows of electrorheological fluids in 3D bounded domains. (February 2019)

• Record Type: Journal Article
• Authors: Sin, Cholmin
• Is Part Of: Nonlinear analysis. Volume 179(2019)
• Page Start: 309
• Page End: 343
• Publication Date: 2019-02
• Subjects: 35D30 -- 35D35 -- 76D03 -- 76A05; Electrorheological fluid -- Weak solution -- Partial regularity -- Regularity up to the boundary -- Variable exponent; 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.2018.08.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we establish boundary partial regularity for weak solutions to the equations of stationary motion of electrorheological fluids with homogeneous Dirichlet boundary condition in 3D bounded smooth domains. We show that there exists an open subset of the boundary such that Hausdorff dimension of it's complementary set is less than 2 and moreover the velocity, it's gradient and the pressure are Hölder continuous in a neighborhood of any point of the set.