Note on quasi-optimal error estimates for the pressure for shear-thickening fluids

Abstract

In this paper, we derive quasi-optimal a priori error estimates for the kinematic pressure for a Local Discontinuous Galerkin (LDG) approximation of steady systems of $p$-Navier--Stokes type in the case of shear-thickening, \textit{i.e.}, $p>2$, imposing a new Muckenhoupt regularity condition on the viscosity of the fluid, which is mild in the two-dimensional case but potentially restrictive in the three-dimensional case.