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GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS

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摘要 This article extends the results of Arkeryd and Cercignani [6]. It is shown that the Cauchy problem for the relativistic Enskog equation in a periodic box has a global mild solution if the mass, energy and entropy of the initial data are finite. It is also found that the solutions of the relativistic Enskog equation weakly converge to the solutions of the relativistic Boltzmann equation in L^1 if the diameter of the relativistic particle tends to zero.
作者 Jianjun HUANG Zhenglu JIANG 黄健骏;姜正禄(Department of Mathematics(Zhuhai),Sun Yat-Sen University,Zhuhai 519082,China;Department of Mathematics,Sun Yat-Sen University,Guangzhou 510275,China)
机构地区 Department of Mathematics(Zhuhai) Department of Mathematics
出处 《Acta Mathematica Scientia》 SCIE CSCD 2020年第5期1335-1351,共17页 数学物理学报（B辑英文版）
基金 supported by NSFC(11171356).
关键词 global existence relativistic Enskog equation relativistic Boltzmann equation
分类号 O411.1 [理学—理论物理]
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  • 1Enskog D. Kinetiche Theorie der Warmeleitung, Reibung und Selbstdiffusion in gewissen werdichteten Gasen und Flubigkeiten. Kungl. Sv. Vetenskapsakademiens Handl, 1922, 63: 3-44, English Transl. in Brush S G, Kinetic Theory. vol 3. New York: Pergamon, 1972.
  • 2Arkeryd L. On the Enskog equation with large initial data. SIAM J. Math. Anal., 1990, 21: 631-646.
  • 3Polewczak J. Global existence and asymptotic behavior for the nonlinear Enskog equation. SIAM J. Appl. Math., 1989, 49: 952-959.
  • 4Polewczak J. On some open problems in the revised Enskog equation for dense gases. In Proceedings "WASCOM 99" 10th Conference on Waves and Stability in Continuous Media, Vulcano (Eolie Islands), Italy, June 7-12, 1999. In: Ciancio V, Donato A, Oliveri F, Rionero S. London: ~Vorld Scientific Publishing, 2001: 382-396.
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  • 6Guo Y. The Vlasov-Poisson-Bolzmann system near vacuum. Comm. Math. Phys., 2001, 218: 293-313.
  • 7Ukai S. Les solutions globales de l'equation de Boltzmann dans l'espace tout entier et dans le demi-espace, C. R. Acad. Sci. Paris Ser. A/B, 1976, 282(6): A317-A320.
  • 8Illner R, Shinbrot M. The Boltzmann equation, global existence for a rare gas in an infinite vacuum. Comm. Math. Phys., 1984, 95: 217-226.
  • 9DiPerna l~ J~ Lions P L. On the Cauchy problem for Boltzmann equations: Global existence and weak stability. Ann. Math., 1989, 130: 321-366.
  • 10Cercignani C. Existence of global solutions for the space inhomogeneous Enskog equation. Transport Theory Statist. Phys., 1987, 16: 213-221.

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Acta Mathematica Scientia
2020年 第5期

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