Opuscula Math. 40, no. 1 (2020), 49-69
https://doi.org/10.7494/OpMath.2020.40.1.49

Opuscula Mathematica

# On the regularity of solution to the time-dependent p-Stokes system

Luigi C. Berselli
Michael Růžička

Abstract. In this paper we consider the time evolutionary $$p$$-Stokes problem in a smooth and bounded domain. This system models the unsteady motion or certain non-Newtonian incompressible fluids in the regime of slow motions, when the convective term is negligible. We prove results of space/time regularity, showing that first-order time-derivatives and second-order space-derivatives of the velocity and first-order space-derivatives of the pressure belong to rather natural Lebesgue spaces.

Keywords: regularity, evolution problem, $$p$$-Stokes.

Mathematics Subject Classification: 76D03, 35Q35, 76A05.

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• Communicated by Vicentiu D. Radulescu.
• Accepted: 2020-01-24.
• Published online: 2020-02-17.