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

TL;DR

This paper proves the local-in-time existence of strong solutions for a broad class of compressible non-Newtonian Navier-Stokes equations with large initial data, extending previous results to more general fluids.

Contribution

It generalizes existing theories by establishing local existence for compressible non-Newtonian fluids using $L^p$-theory and the Weis multiplier theorem.

Findings

Established local-in-time strong solutions for large initial data.

Extended previous results to non-Newtonian compressible fluids.

Utilized $L^p$-theory and multiplier theorems for analysis.

Abstract

The aim of this article is to show a local-in-time existence of a strong solution to the generalized compressible Navier-Stokes equation 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 generalization of the work of Shibata and Enomoto (devoted to compressible fluids) to compressible non-Newtonian fluids.