Jianjun HUANG
,
Zhenglu JIANG
. GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS[J]. Acta mathematica scientia, Series B, 2020
, 40(5)
: 1335
-1351
.
DOI: 10.1007/s10473-020-0511-0
[1] Adams R A. Sobolev Space. New York:Academic Press, 1975
[2] Andréasson H. Regularity of the gain term and strong L1 convergence to the equilibrium for the relativistic Boltzmann equation. SIAM J Math Anal, 1996, 27:1386-1405
[3] Arkeryd L. On the Enskog equation in two space variables. Transport Theory Stat Phys, 1986, 15:673-691
[4] Arkeryd L. On the Enskog equation with large initial data. SIAM J Math Anal, 1990, 21:631-646
[5] Arkeryd L, Cercignani C. On the convergence of solutions of the Enskog equation to the solutions of the Boltzmann equation. Commun Partial Differ Equ, 1989, 14:1071-1089
[6] Arkeryd L, Cercignani C. Global existence in L1 for the Enskog equation and the convergence of the solutions to solutions of the Boltzmann equation. J Stat Phys, 1990, 59:845-867
[7] Bellomo N. Mathematical Topics in Nonlinear Kinetic Theory Ⅱ:the Enskog Equation. Singapore:World Sci, 1991
[8] Bellomo N, Lachowicz M. On the asymptotic equivalence between the Enskog and the Boltzmann equations. J Stat Phys, 1988, 51:233-247
[9] Bichteler K. On the Cauchy problem of the relativistic Boltzmann equations. Commun Math Phys, 1967, 4:352-364
[10] Cercignani C. H-theorem and trend to equilibrium in the kinetic theory of gases. Arch Mech, 1982, 34:231-241
[11] Cercignani C. Existence of global solutions for the space inhomogeneous Enskog equation. Transport Theory Stat Phys, 1987, 16:213-221
[12] Cercignani C. Small Data Existence for the Enskog equation in L1. J Stat Phys, 1988, 51:291-297
[13] Cercignani C, Kermer G. The Relativistic Boltzmann Equation, Theory and Application. Boston:Birkhaeuser, 2002
[14] Chapman T, Cowling T G. The Mathematical Theory of Non-uniform Gases. Third ed. Cambridge University Press, 1970
[15] de Groot S R, Van Leeuwen W A, Van Weert Ch G. Relativistic Kinetic Theory. Amsterdam:NorthHolland, 1980
[16] DiPerna R J, Lions P L. On the Cauchy problem for Boltzmann equations:Global existence and weak stability. Ann Math, 1989, 130:321-366
[17] Dudyński M, Ekiel-Je·zewska M L. On the linearized relativistic Boltzmann equation. Commun Math Phys, 1988, 115:607-629
[18] Dudyński M, Ekiel-Jezewska M L. Global existence proof for the relativistic Boltzmann equation. J Statist Phy, 1992, 66:991-1001
[19] Dunford N, Schwartz J T. Linear Operator, I. Interscience, 1963
[20] Enskog D. Kinetiche Theorie der Wàrmeleitung, 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
[21] Esteban M J, Perthame B. On the modified Enskog equation for elastic and inelastic collisions, models with spin. Ann Inst H Poincare Anal, 1991, 8:289-308
[22] Glassey R. Global solutions to the Cauchy problem for the relativistic Boltzmann equation with nearvacuum data. Commun Math Phys, 2006, 264:705-724
[23] Glassey R, Strauss W. On the derivatives of the collision map of relativistic particles. Transport Theory Stat Phys, 1991, 20:55-68
[24] Glassey R, Strauss W. Asymptotic stability of the relativistic Maxwellian. Publ Res Inst Math Sci, 1993, 29:301-347
[25] Glassey R, Strauss W. Asymptotic stability of the relativistic Maxwellian via fourteen moments. Transport Theory Stat Phys, 1995, 24:657-678
[26] Golse F, Lions P L, Perthame B, Sentis R. Regularity of the moments of the solution of a transport equation. J Funct Anal, 1988, 76:110-125
[27] Ha S. Lyapunov functionals for the Enskog-Boltzmann equation. Indiana Univ Math J, 2005, 54:997-1014
[28] Jiang Z. On the relatvistic Boltzmann equation. Acta Mathematica Scientia, 1998, 18:348-360
[29] Jiang Z. Existence of global solution to the Cauchy problem for the relativistic Boltzmann equation in a periodic box. Acta Mathematica Scientia, 1998, 18:375-384
[30] Jiang Z. On Cauchy problem for the relatvistic Boltzmann equationin a periodic box:global existence. Transport Theory Stat Phys, 1999, 28:617-628
[31] Jiang Z. Global Solution to the relativistic Enskog equation with near-vacuum. J Stat Phys, 2007, 127:805-812
[32] Jiang Z. Global existence proof for relativistic Boltzmann equation with hard interactions. J Stat Phys, 2009, 130:49-62
[33] Jiang Z. Global Solution to the Enskog equation with external force in infinite vacuum. Chinese Journal of Contemporary Mathematics, 2009, 127:805-812
[34] Jiang Z, Ma L, Yao Z. Stability of global solution to Boltzmann-Enskog equation with external force. Communications in Mathematical Research, 2012, 28:108-120
[35] Kaniel S, Shinbrot M. The Boltzmann Equation I. Uniqueness and local existence. Comm Math Phys, 1978, 58:65-84
[36] Lachowicz M. On the local existence and uniqueness of solution of initial-value problem for the Enskog equation. Bull Pol Acad Sci, 1983, 31:89-96
[37] Polewczak J. Global existence and asymptotic behavior for the nonlinear Enskog equation. SIAM J Appl Math, 1989, 49:952-959
[38] Polewczak J. Global existence in L1 for the modified nonlinear Enskog equation in R3. J Stat Phys, 1989, 56:159-173
[39] Polewczak J. Global existence in L1 for the generalized Enskog equation. J Stat Phys, 1989, 59:461-500
[40] Strain R M. Global Newtonian limit for the relativistic Boltzmann equation near vacuum. SIAM J Math Anal, 2010, 42(4):1568-1601
[41] Strain R M. Asymptotic stability of the relativistic Boltzmann equantion for the soft potentials. Commun Math Phys, 2010, 300:529-597
[42] Strain R M. Coordinates in the relativistic Boltzmann theory. Kinetic and Related Models, 2011, 4(1):345-359
[43] Toscani G, Bellomo N. The Enskog-Boltzmann equation in the whole space R3:Some global existence, uniqueness and stability results. Comput Math Appl, 198713:851-859
[44] Wu Z. Stability of global solution for the relativistic Enskog equation near vacumm. J Stat Phys, 2009, 137:149-164
