On the cauchy problem for Landau equation: Sequential stability, global existence

Advances in Differential Equations

Volumn 1, Issue 5, 1996, Pages 793-816

  Villani, Cédric ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

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[No Author keywords available]

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EID: 0013297897     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: 10.57262/ade/1366896020     Document Type: Article

References (21)

1. A.A. Arsen'ev and O.E. Buryak, On the connection between a solution of the Boltzmann equation and a solution of the Landau-Fokker-Planck equation, Math. USSR Sbornik, 69 (1991), 465-478.
2. 1 data: existence and uniqueness, preprint, 1995.
3. L. Boltzmann, Weitere Studienüber das Wärme gleichgenicht unter Gasmolekülen, 1872.
4. C. Cercignani, "The Boltzmann Equation and its Applications," Springer, New York, 1988.
5. C. Cercignani, R. Illner, and M. Pulvirenti, "The Mathematical Theory of Dilute Gases," Springer-Verlag, 1994.
6. S. Chapman and T.G. Cowling, "The Mathematical Theory of Non-Uniform Gases," Cambridge University Press, 1952.
7. P. Degond and B. Lucquin-Desreux, The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case, Math. Mod. Meth. in Appl. Sci., 2 (1992), 167-182.
8. L. Desvillettes, Convergence to equilibrium in various situations for the solution of the Boltzmann equation, Nonlinear Kin. Th. and Math. Aspects of Hyp. Syst., Series on Adv. in Math. for Appl. Sci., 9 (1992), 101-114.
9. L. Desvillettes, On asymptotics of the Boltzmann equation when the collisions become grazing, Transp. Theory and Stat. Phys., 21 (1992), 259-276.
10. R.J. Di Perna and P.L. Lions, On the Fokker-Planck-Boltzmann equation, Commun. Math. Phys. 120 (1988), 1-23.
11. R.J. Di Perna and P.L. Lions, On the Cauchy problem for the Boltzmann equation: global existence and weak stability, Ann. Math., 130 (1989), 312-366.
12. R.J. Di Perna and P.L. Lions, Global solutions of Boltzmann's equation and the entropy inequality, Arch. Rat. Mech. Anal., 114 (1991), 47-55.
13. p regularity of velocity averages, Ann. IHP, 114 (1991), 271-287.
14. K. Hamdache, Initial boundary value problems for the Boltzmann equation: global existence of weak solutions, Arch. Rat. Mech. Anal., 119 (1992), 309-353.
15. E.M. Lifchitz and L.P. Pitaevskii, Physical Kinetics-Course of Theoretical Physics," vol. 10, Pergamon, Oxford, 1981.
16. P.L. Lions, On Boltzmann and Landau equations, Phil. Trans. R. Soc. Lond., 346A (1994), 191-204.
17. P.L. Lions and C. Villani, Régularité optimale de racines carrées, C.R. Acad. Sci. Paris, t. 321, Série I (1995), 1537-1541.
18. J.C. Maxwell, On the dynamical theory of gases, Phil. Trans. R. Soc. Lond., 157 (1886), 49-88.
19. J.C. Maxwell, "Scientific Papers," vol. 2, reprinted by Dover Publications, New York, 1890.
20. C. Truesdell and R.G. Muncaster, "Fundamentals of Maxwell's Kinetic Theory of a Simple Monoatomic Gas," Academic Press, New York, 1980.
21. A.M. Il'in, On a class of ultraparabolic equations, Sov. Math. Dokl., 5 (1964), 1673-1676.