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

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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… Click to show full 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: system; regularity solution; time; time dependent; solution time

Journal Title: Opuscula Mathematica
Year Published: 2020

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