Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Zihui He

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.

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

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.
Paper Structure (4 sections, 2 theorems, 49 equations)

This paper contains 4 sections, 2 theorems, 49 equations.

Table of Contents

  1. Introduction
  2. Main result
  3. Other symmetric solutions
  4. Proof of existence

Key Result

Theorem 1.1

Let $b\in C(\mathbb{R};[\mu_\ast,\mu^*])$, $\mu_\ast,\mu^*>0$ and $\eta\in L^\infty(\mathbb{R};[\rho_*,\rho^*])$, $0<\rho_\ast\leq \rho^\ast$ be given. Let $\Omega$ be a bounded connected axially symmetric domain defined as in domian:R3. Let $u_0\in H^{1/2}_\sigma(\partial\Omega)=\{\text{tr}(u) \mid of the boundary value problem SNS3--u00:R3, where $\varphi\in H^2(\Omega)$ is an axially symmetric

Theorems & Definitions (6)

  • Theorem 1.1
  • Remark 1.2
  • Theorem 1.3
  • proof
  • Remark 1.4
  • Remark 2.1