Abstract
We consider the regularity of weak solutions to the shear thinning fluids in \({\mathbb {R}}^{3}\). Let u be a weak solution in \({\mathbb {R}}^{3}\times (0,T)\) and \(\widetilde{u}=(u_{1},u_{2},0)\). It is proved that u becomes a strong solution if \(\widetilde{u}\in L^{\frac{5p-6}{5p-8}}(0,T;BMO({\mathbb {R}}^{3}))\) , for \(\frac{8}{5}<p\le 2\). This is an improvement of the result given by Yang (Comput Math Appl 77:2854–2858).
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Acknowledgements
This work was done while S. GALA visited the University of Catania, Italy. He is grateful for the hospitality and support of the University. This research is partially supported by P.R.I.N. 2019. The third author wish to thank the support of “RUDN University Program 5-100”. The authors would like to thank the referees for their valuable comments and remarks.
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Alghamdi, A.M., Gala, S., Ragusa, M.A. et al. Regularity criterion via two components of velocity on weak solutions to the shear thinning fluids in \({{\mathbb {R}}}^{3}\). Comp. Appl. Math. 39, 234 (2020). https://doi.org/10.1007/s40314-020-01281-w
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DOI: https://doi.org/10.1007/s40314-020-01281-w