Global existence of shock front solution to axially symmetric piston problem in compressible flow

作者：Chen Shuxing^*; Wang Zejun; Zhang Yongqian

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2008, 59(3): 434-456.

DOI：10.1007/s00033-007-6010-5

• piston problem
• Glimm scheme
• Euler system
• shock front solution
• Riemann problem
• interaction of elementary waves

In this paper we study the global existence of BV solution to two-dimensional piston problem in fluid dynamics. Different from previous results on related problems we remove the restriction on the strength of the leading shock and require the velocity of the piston is rather fast or the density is quite small instead. The main tool in our proof is Glimm Scheme with some improvement. To define the Glimm functional we derive more precise estimates for the interaction of elementary waves, particularly in the region near the leading shock.

• 出版日期2008-5
• 单位复旦大学