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GLOBAL STABILITY OF SOLUTIONS WITH DISCONTINUOUS INITIAL DATA CONTAINING VACUUM STATES FOR THE RELATIVISTIC EULER EQUATIONS 被引量：4

GLOBAL STABILITY OF SOLUTIONS WITH DISCONTINUOUS INITIAL DATA CONTAINING VACUUM STATES FOR THE RELATIVISTIC EULER EQUATIONS
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摘要 The global stability of Lipschitz continuous solutions with discontinuous initial data for the relativistic Euler equations is established in a broad class of entropy solutions in L∞ containing vacuum states. As a corollary, the uniqueness of Lipschitz solutions with discontinuous initial data is obtained in the broad class of entropy solutions in L∞.
作者 LI YACHUN WANG LIBO
机构地区 Department of Mathematics
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2005年第4期491-510,共20页 数学年刊（B辑英文版）
基金 Project supported by the National Natural Science Foundation of China (No.10101011) the Natural Science Foundation of Shanghai (No.04ZR14090).
关键词 Relativistic Euler equations Entropy solutions VACUUM UNIQUENESS Global stability EULER方程 熵解 真空状态 唯一性 初始值 稳定性
分类号 O175 [理学—基础数学]
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参考文献30

  • 1Chang, T. & Hsiao, L., The Riemann Problem and Interaction of Waves in Gas Dynamics, Longman Scientific & Technical, Harlow; and John Wiley & Sons, Inc., New York, 1989.
  • 2Chen, G. Q., Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (Ⅲ), Acta Math. Sci., 6(1986), 75-120 (in English); and 8(1988), 243-276 (in Chinese).
  • 3Chen, G. Q., Vacuum states and global stability of rarefaction waves for compressible flow, Methods Appl. Anal., 7(2000), 337-361.
  • 4Chen, G. Q., & Frid, H., Divergence-measure fields and conservation laws, Arch. Rational Mech. Anal., 147(1999), 89-118; Extended divergence-measure fields and the Euler equations for gas dynamics, Comm. Math. Phys., 236(2003), 251-280.
  • 5Courant, R., & Friedrichs, K. O., Supersonic Flow and Shock Waves, Interscience, New York, 1948.
  • 6Chen, G. Q. & Frid, H., Uniqueness and asymptotic stability of Riemann solutions for the compressibleEuler equations, Trans. Amer. Math. Soc., 353(2001), 1103-1117.
  • 7Chen, G. Q. & Frid, H., Large-time behavior of entropy solutions of conservation laws, J. Diff. Eqs., 152(1999), 308-357.
  • 8Chen, G. Q., Frid, H. & Li, Y. C., Uniqueness and stability of Riemann solutions with large oscillation in gas dynamics, Commun. Math. Phys., 228(2002), 201-217.
  • 9Chen, G. Q. & LeFloch, P., Compressible Euler equation with general pressure law, Arch. Rational Mech. Anal., 153(2000), 221-259.
  • 10Chen, G. Q. & Li, Y. C., Stability of Riemann solutions with large oscillation for the relativistic Euler equations, J. Differential Equations, 202(2004), 332-353.

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Chinese Annals of Mathematics,Series B
2005年 第4期

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