We construct classical self-similar solutions to the interaction of two arbitrary planar
rarefaction waves for the polytropic Euler equations in two space dimensions. The binary …

The global existence and structures of solutions to multi-dimensional unsteady compressible
Euler equations are interesting and important open problems. In this paper, we construct …

We construct semi-hyperbolic patches of solutions, in which one family out of two nonlinear
families of characteristics starts on sonic curves and ends on transonic shock waves, to the …

This paper is concerned with classical solutions to the interaction of two arbitrary planar
rarefaction waves for the self-similar Euler equations in two space dimensions. We develop …

This paper focuses on the structure of classical sonic-supersonic solutions near sonic curves
for the two-dimensional full Euler equations in gas dynamics. In order to deal with the …

It is perhaps surprising for a shock wave to exist in the solution of a rarefaction Riemann
problem for the compressible Euler equations in two space dimensions. We present …

We construct classical self-similar solutions to the interaction of two arbitrary planar
rarefaction waves for the Euler equations in two space dimensions via the characteristics …

We construct patches of self-similar solutions, in which one family out of two nonlinear
families of characteristics starts on sonic curves and ends on transonic shock waves, to the …

We present two new types of self-similar solutions to the Chaplygin gas model in two space
dimensions: Simple waves and pressure delta waves, which are absent in one space …

Given a smooth curve as a sonic line in the plane, we construct a local smooth supersonic
solution on one side of the curve for the steady compressible Euler system of equations in …