We establish regularity results for solutions of a generalized Newtonian model in a cubic domain. We prove regularity results in the L2-space for the second derivatives of the velocity and the first derivatives of the pressure. Further, we show that the gradient of weak solutions is integrable up to the boundary with any finite exponent.
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Francesca Crispo, A note on the global regularity of steady flows of generalized Newtonian fluids. Port. Math. 66 (2009), no. 2, pp. 211–223DOI 10.4171/PM/1841