A complete global solution to the pressure gradient equation

作者：Lei Zhen; Zheng Yuxi^*

来源：Journal of Differential Equations, 2007, 236(1): 280-292.

DOI：10.1016/j.jde.2007.01.024

• regularity
• vacuum boundary
• two-dimensional Riemann problem
• characteristic decomposition
• gas dynamics
• shock waves
• enter equations
• Goursat problem

We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes.

• 出版日期2007-5-1
• 单位东北师范大学; 复旦大学