Premium
Regularity in Sobolev spaces of steady flows of fluids with shear‐dependent viscosity
Author(s) -
Ebmeyer Carsten
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.748
Subject(s) - sobolev space , mathematics , bounded function , domain (mathematical analysis) , viscosity , mathematical analysis , boundary value problem , pressure gradient , order (exchange) , pure mathematics , physics , mechanics , thermodynamics , finance , economics
The system$${-{\rm{div}}\,{\rm\bf{S}}({\rm\bf{D}}({\rm\bf{u}}))+({\rm\bf{u}}\cdot\nabla){\rm\bf{u}}+\nabla\pi\,{=}\,{\rm\bf{f}}, \quad{\rm{div}}\,{\rm\bf{u}}\,{=}\,0}$$is considered on a bounded three‐dimensional domain under no‐stick boundary value conditions, where S has p ‐structure for some p <2 and D ( u ) is the symmetrized gradient of u . Various regularity results for the velocity u and the pressure π in fractional order Sobolev and Nikolskii spaces are obtained. Copyright © 2006 John Wiley & Sons, Ltd.