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Local Existence of the Shock Front Solution to the Axi-symmetrical Piston Problem in Compressible Flow 被引量：4

Local Existence of the Shock Front Solution to the Axi-symmetrical Piston Problem in Compressible Flow
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摘要 In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in com- pressible flow.The corresponding mathematical model is the well-known Euler system.With the Newton iteration procedure and energy estimate,we give the local existence of the shock front solution to this problem. In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in com- pressible flow.The corresponding mathematical model is the well-known Euler system.With the Newton iteration procedure and energy estimate,we give the local existence of the shock front solution to this problem.
作者 ZeJunWANG
机构地区 InstituteofMathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第4期589-604,共16页 数学学报（英文版）
基金 Supported partially by NSFC Project 10131050 and NSFC Project 10271108
关键词 Piston problem Euler system Shock front solution Newton iteration Energy estimate Piston problem Euler system Shock front solution Newton iteration Energy estimate
分类号 O175.24 [理学—基础数学]
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参考文献12

  • 1Whitham, G. B.: Linear and nonlinear waves. Wiley, New York, London, Sydney, Toronto, 1974.
  • 2Chen, S. X.: A singular multi-dimensional piston problem ill compressible flow. Jour. Diff. Eqns., 189,292-317 (2003).
  • 3Chen, S. X., Wang, Z. J., Zhang, Y. Q.: Global existence of shock front solutions for the axially symmetric piston problem for compressible fluids.Jour. Hyper. Diff. Eqns., 1(1), 51-84 (2004).
  • 4CouranL R., Friedrichs, K. O.: Supersonic flow and shock waves, Interscience Publishers Inc., New York,1948.
  • 5Chen, G. Q.: Remarks on spherically symmetric solution of the compressible euler equation. Proceedings of the Royal Society of Edinburgh, 127A, 243-259 (1997).
  • 6Chen, S. X.: Existence of stationary supersonic flow past a pointed body. Arch. Rational Mech. Anal.,149(2), 141-181 (2001).
  • 7Chen, S. X., Li, D. N.: Supersonic flow past a symmetrically curved cone. Indiana Univ. Math. Jour.,49(4), 1411-1435 (2000).
  • 8Lien, W. C., Liu T. P.: Nonlinear stability of a self-somilar 3-D gas flow. Comm. Math. Phys, 304,524-549( 1999).
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  • 10Zhang, Y. Q.: Global existence of steady supersonic potential flow past a curved wedge with piecewise smooth boundary. SlAM J. Math. Anal., 31(1), 166-183 (1999).

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Acta Mathematica Sinica,English Series
2004年 第4期

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