On the partial regularity of suitable weak solutions in the non-Newtonian shear-thinning case

We study the partial regularity of suitable weak solutions to incompressible non-Newtonian fluids in the shear-thinning case p < 2. For the shear-thickening case p > 2 this problem was previously considered in 2002 by Guo and Zhu (J. Differ. Equ. 178 281--97). By partially appealing to some of...

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Bibliographic Details
Published in:Nonlinearity 2021-01, Vol.34 (1), p.562-577
Main Authors: Beirão da Veiga, Hugo, Yang, Jiaqi
Format: Article
Language:English
Subjects:
non-Newtonian fluids
partial regularity
shear-thinning
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Summary:We study the partial regularity of suitable weak solutions to incompressible non-Newtonian fluids in the shear-thinning case p < 2. For the shear-thickening case p > 2 this problem was previously considered in 2002 by Guo and Zhu (J. Differ. Equ. 178 281--97). By partially appealing to some of their ideas, we show that in the p < 2 case the singular points are concentrated on a closed set whose one dimensional Hausdorff measure is zero.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/abcd06