Preprint 2005-011

Two-dimensional regular shock reflection for the pressure gradient system of conservation laws

Yuxi Zheng

Abstract: We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach's experiment for the compressible Euler system, i.e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.

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Yuxi Zheng, <>
Publishing information:
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<> February 7 2005.

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