On steady flow of non-Newtonian fluids with frictional boundary conditions in reflexive Orlicz spaces

• Published in: Nonlinear analysis: real world applications Vol. 39; pp. 337 - 361
• Main Authors: Migórski, Stanisław, Pączka, Dariusz
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.02.2018; Elsevier BV
• Subjects: Boundary conditions; Computational fluid dynamics; Fluid flow; Frictional boundary condition; Hemivariational inequality; Incompressible flow; Newtonian fluids; Non Newtonian fluids; Non-Newtonian fluid; Orlicz space; Pseudomonotone operator; Sobolev space; Steady flow; Uniqueness; Hemivariational inequality; Orlicz space; Pseudomonotone operator; Frictional boundary condition; Non-Newtonian fluid
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2017.07.003

A stationary viscous incompressible non-Newtonian fluid flow problem is studied with a non-polynomial growth of the extra (viscous) part of the Cauchy stress tensor together with a multivalued nonmonotone frictional boundary condition described by the Clarke subdifferential. We provide an abstract result on existence of solution to a subdifferential operator inclusion and a hemivariational inequality in the reflexive Orlicz–Sobolev space setting modeling the flow phenomenon. We establish the existence result, and under additional conditions, also uniqueness of a weak solution in the Orlicz–Sobolev space to the flow problem.