On a degenerate hyperbolic problem for the 3-D steady full Euler equations with axial-symmetry

Yanbo Hu,Fengyan Li

doi:10.1515/anona-2020-0148

Abstract

AbstractThe transonic channel flow problem is one of the most important problems in mathematical fluid dynamics. The structure of solutions near the sonic curve is a key part of the whole transonic flow problem. This paper constructs a local classical hyperbolic solution for the 3-D axisymmetric steady compressible full Euler equations with boundary data given on the degenerate hyperbolic curve. By introducing a novel set of dependent and independent variables, we use the idea of characteristic decomposition to transform the axisymmetric Euler equations as a new system which has explicitly singularity-regularity structures. We first establish a local classical solution for the new system in a weighted metric space and then convert the solution in terms of the original variables.

Highlights

The three-dimensional steady compressible full Euler equations read that [12]x +y +z =+ p)x +y +z =(ρu u )x +y +z =, (1.1)x +
The structure of solutions near the sonic curve is a key part of the whole transonic ow problem
This paper constructs a local classical hyperbolic solution for the 3-D axisymmetric steady compressible full Euler equations with boundary data given on the degenerate hyperbolic curve

Summary

Introduction

This paper constructs a local classical hyperbolic solution for the 3-D axisymmetric steady compressible full Euler equations with boundary data given on the degenerate hyperbolic curve. On a degenerate hyperbolic problem for the 3-D steady full Euler equations (u, v, w)(x, r) and p(x, r) in cylindrical coordinates (x, r, σ), where u, v, w are, respectively, the axial velocity, radial velocity and swirl velocity, that is, u = u, u = cos σ − sin σ u sin σ cos σ v.

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