Solvability of the two-dimensional stationary incompressible inhomogeneous Navier-Stokes equations with variable viscosity coefficient

Abstract

We show the existence and the regularity properties of the weak solutions to the two-dimensional stationary incompressible inhomogeneous Navier-Stokes equations with variable viscosity coefficient, by analyzing a fourth-order nonlinear elliptic equation for the stream function. The density function and the viscosity coefficient may have large variations. In addition, we formulate the solutions for the parallel, concentric and radial flows respectively, and as examples we calculate the solutions with piecewise-constant viscosity coefficients explicitly.

arXiv commentThe structure of the paper is updated. Some corrections are made in the proof of Theorem 1.5

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Cited by in corpus (2)

• On variable viscosity and enhanced dissipation
• A Note On Determining Projections for Non-Homogeneous Incompressible Fluids