On the steady non-Newtonian fluids in domains with noncompact boundaries

TL;DR

This paper investigates the mathematical behavior of non-Newtonian fluids in unbounded domains with noncompact boundaries, establishing conditions for existence and uniqueness of solutions based on flux size.

Contribution

It extends previous results by proving global existence for large flux and uniqueness for small flux in complex unbounded domains.

Findings

Global existence of solutions with arbitrary large flux

Uniqueness of solutions when flux is sufficiently small

Improved understanding of non-Newtonian fluid behavior in unbounded domains

Abstract

In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under some suitable conditions, and meanwhile, show the uniqueness of the solutions when the flux is sufficiently small. Our results are an extension or an improvement of those obtained in some previous references.