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

Abstract

The 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.

Keywords

• full euler equations
• axial-symmetry
• degenerate hyperbolic
• classical solution
• characteristic decomposition
• 35l65
• 35l80
• 76h05