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Boundary Partial \(C^{1, \alpha }\)-Regularity for Stationary Shear Thickening Flows in 3D

  • Cholmin Sin
Article

Abstract

In this paper, we prove boundary partial regularity result for weak solutions to systems describing stationary shear thickening flows in 3D smooth domains. We show that the weak solution is in \(C^{1,\,\alpha }\) with any \(\alpha \in (0,\,1)\) in a neighbourhood of almost all boundary points. In particular, we show that for the regularity criterion at the boundary, only the normal derivative is of importance.

Keywords

Generalized Newtonian fluid Shear thickening fluid Partial regularity Regularity up to the boundary 

Mathematics Subject Classification

35D30 35D35 76D03 76A05 

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Notes

Acknowledgements

The author would like to thank the editor and the anonymous referee for their valuable suggestions to improve the quality of this paper and to make the presentation more readable.

Compliance with ethical standards

Conflict of interest

No conflict of interest to be declared by the author.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of MathematicsAcademy of SciencesPyongyangDemocratic People’s Republic of Korea

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