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 f...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 three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.展开更多
The 'hole-boring problem'in ECM is considered.It is shown that after a finite period of time the free boundary becomes smooth in space variables and Holder continuous in time variable without imposing specific...The 'hole-boring problem'in ECM is considered.It is shown that after a finite period of time the free boundary becomes smooth in space variables and Holder continuous in time variable without imposing specific geometric assumption on the initial and boundary data.展开更多
基金Partially supported by NSF-DMS-0305497 and 0305114.
文摘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 three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.
文摘The 'hole-boring problem'in ECM is considered.It is shown that after a finite period of time the free boundary becomes smooth in space variables and Holder continuous in time variable without imposing specific geometric assumption on the initial and boundary data.
