Steady flow for incompressible fluids in domains with unbounded curved channels

TL;DR

This paper reviews solutions to the stationary Navier-Stokes equations for non-Newtonian incompressible fluids in complex unbounded curved channels, proposing a new domain definition and discussing steady flow existence for arbitrary fluxes.

Contribution

It introduces a comprehensive domain definition for unbounded curved channels and discusses the existence of steady flows for non-Newtonian fluids with arbitrary fluxes.

Findings

Existence of steady flow in complex unbounded domains.

A new domain definition encompassing various geometries.

Extension of previous results to non-Newtonian fluids.

Abstract

We give an overview on the solution of the stationary Navier-Stokes equations for non newtonian incompressible fluids established by G. Dias and M.M. Santos (Steady flow for shear thickening fluids with arbitrary fluxes, J. Differential Equations 252 (2012), no. 6, 3873-3898)*, propose a definition for domains with unbounded curved channels which encompasses domains with an unbounded boundary, domains with nozzles, and domains with a boundary being a punctured surface, and argue on the existence of steady flow for incompressible fluids with arbitrary fluxes in such domains. *Cf. ArXiv: 1108.3595.