Weak solutions to stationary motions of shear thinning fluids with nonhomogeneous Dirichlet boundary conditions. (July 2021)

• Record Type: Journal Article
• Authors: Elshehabey, Hillal M.; Silvestre, Ana L.
• Is Part Of: Nonlinear analysis. Volume 208(2021)
• Publication Date: 2021-07
• Subjects: 35Q35 -- 76D03 -- 35J92; Shear thinning fluids -- Steady state -- Nonhomogeneous Dirichlet boundary conditions -- Weak solutions -- Solenoidal extension -- Distance-to-boundary function; 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.2021.112277
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider steady flows of shear thinning fluids in bounded domains under the action of external forces and Dirichlet boundary conditions. For a power-law index q ∈ ( 2 d ∕ ( d + 2 ), 3 d ∕ ( d + 2 ) ], we construct weak solutions to the nonhomogeneous boundary value problem assuming that the boundary data is small enough. Moreover, under the restriction q ∈ ( ( 2 d − 1 ) ∕ d, 2 ), d = 2, 3, and extra regularity for the boundary data, we construct weak solutions by extending the tangential part of the velocity at the boundary in such a way that it is possible to partially control the inertial term. This imposes restrictions only on the size of the normal component of the boundary data.