Three-dimensional stationary incompressible inhomogeneous Navier-Stokes equation in the axially symmetric case

TL;DR

This paper proves the existence of weak solutions for the 3D stationary inhomogeneous Navier-Stokes equations with density-dependent viscosity under axial symmetry, extending to various coordinate systems.

Contribution

It establishes the existence of weak solutions in the axially symmetric case for inhomogeneous Navier-Stokes equations with density-dependent viscosity, a novel result in this setting.

Findings

Existence of weak solutions in axial symmetry

Extension to cylindrical, spherical, and Cartesian coordinates

Analysis of density-dependent viscosity effects

Abstract

We show the existence of (a class of) weak solutions to the three-dimensional stationary incompressible inhomogeneous Navier--Stokes equations with density-dependent viscosity coefficient in the axially symmetric case. Further symmetric solutions in cylindrical coordinates, spherical coordinates and Cartesian coordinates are also discussed.