Global existence of shock front solution to axially symmetric piston problem in compressible flow |
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| Authors: | Shuxing Chen Zejun Wang and Yongqian Zhang |
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| Institution: | (1) Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, WY 82070, USA;(2) Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA 90089, USA;(3) Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA |
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| Abstract: | 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. |
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