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.
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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.
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Sin, C. Boundary Partial \(C^{1, \alpha }\)-Regularity for Stationary Shear Thickening Flows in 3D. J. Math. Fluid Mech. 20, 1617–1639 (2018). https://doi.org/10.1007/s00021-018-0379-0
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DOI: https://doi.org/10.1007/s00021-018-0379-0