Local-in-time existence of strong solutions to a class of the compressible non-Newtonian Navier–Stokes equations

Abstract

The aim of this article is to show a local-in-time existence of a strong solution to the generalized compressible Navier-Stokes equations for arbitrarily large initial data. The goal is reached by \(L^p\)-theory for linearized equations which are obtained with help of the Weis multiplier theorem and can be seen as a generalization of the work of Enomoto and Shibata (Funkcial Ekvac 56(3):441–505, 2013) (devoted to compressible fluids) to compressible non-Newtonian fluids.