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Flow of shear dependent electrorheological fluids: Unsteady space periodic case. (English) Zbl 0954.35138
Sequeira, Adélia (ed.) et al., Applied nonlinear analysis. In honor of the 70th birthday of Professor Jindřich Nečas. New York, NY: Kluwer Academic/Plenum Publishers. 485-504 (1999).
Summary: We study the existence of weak and strong solutions to the unsteady and steady system of partial differential equations \[ \text{div }{\mathbf E}= 0, \] \[ \text{curl }{\mathbf E}= 0, \] \[ {\partial{\mathbf v}\over\partial t}- \text{div }{\mathbf S}+ [\nabla{\mathbf v}]{\mathbf v}+ \nabla \pi={\mathbf f}+ \chi^E[\nabla{\mathbf E}]{\mathbf E}, \] \[ \text{div }{\mathbf v}=0, \] with non-standard growth conditions describing the flow of shear dependent electrorheological fluids in the case of space periodic boundary conditions.
For the entire collection see [Zbl 0939.00054].

35Q35 PDEs in connection with fluid mechanics
76A05 Non-Newtonian fluids
76W05 Magnetohydrodynamics and electrohydrodynamics