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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- Luigi C. Berselli (corresponding author)
https://orcid.org/0000-0001-6208-9934- Università di Pisa, Dipartimento di Matematica, Via F. Buonarroti 1/c, I-56127 Pisa, Italy
- Michael Růžička
- https://orcid.org/0000-0001-8497-1864
- Albert-Ludwigs-University Freiburg, Institute of Applied Mathematics, Ernst-Zermelo-Str. 1, D-79104 Freiburg, Germany
- Communicated by Vicentiu D. Radulescu.
- Received: 2019-12-22.
- Accepted: 2020-01-24.
- Published online: 2020-02-17.
