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

Berselli Luigi C., Ruzicka Michael

Opuscula Mathematica

2020

Vol. 40, no. 1

49--69

n 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.