A Local Discontinuous Galerkin approximation for the $p$-Navier-Stokes system, Part III: Convergence rates for the pressure

In the present paper, we prove convergence rates for the pressure of the Local Discontinuous Galerkin (LDG) approximation, proposed in Part I of the paper, of systems of $p$-Navier-Stokes type and $p$-Stokes type with $p\in (2,\mathrm{\infty })$. The results are supported by numerical experiments.