A note on the global regularity of steady flows of generalized Newtonian fluids

Crispo, Francesca

doi:10.4171/PM/1841

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Portugaliae Mathematica

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Volume 66, Issue 2, 2009, pp. 211–223

DOI: 10.4171/PM/1841

Published online: 2009-06-30

A note on the global regularity of steady flows of generalized Newtonian fluids

Francesca Crispo^[1]

(1) Università di Pisa, Italy

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.

Keywords: Generalized Newtonian fluids, shear thinning fluids, global regularity

Crispo Francesca: A note on the global regularity of steady flows of generalized Newtonian fluids. Port. Math. 66 (2009), 211-223. doi: 10.4171/PM/1841