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Article
Simple Waves and a Characteristic Decomposition of the Two Dimensional Compressible Euler Equations
We present a characteristic decomposition of the potential flow equation in the self-similar plane. The decomposition allows for a proof that any wave adjacent to a constant state is a simple wave for the adia...
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Article
Interaction of Rarefaction Waves of the Two-Dimensional Self-Similar Euler Equations
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 interaction represents a major ...
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Article
Interaction of Four Rarefaction Waves in the Bi-Symmetric Class of the Two-Dimensional Euler Equations
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 global classical solutions t...
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Article
Sonic-Supersonic Solutions for the Two-Dimensional Steady Full Euler Equations
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 parabolic degeneracy near t...