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Young measure-valued solutions for non-Newtonian incompressible fluids. (English) Zbl 0840.35079
This paper deals with the problem of a nonlinear bipolar fluid, in which the higher-order viscosity vanishes, and the viscous part of the stress tensor satisfies a growth condition of the form \[ |\tau_{ij}|\leq C(1+ |e|)^{p- 1},\quad C> 0, \] \(e\) the rate of strain tensor. The authors give some existence results of Young-measure valued solutions, which under certain limitations on \(p\) depending on the space dimensions are also weak solutions. Uniqueness is also guaranteed for higher values of \(p\).
Reviewer: F.Rosso (Firenze)

MSC:
35Q35 PDEs in connection with fluid mechanics
35D05 Existence of generalized solutions of PDE (MSC2000)
76A05 Non-Newtonian fluids
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