摘要Global-in-time classical solutions near Maxwellians with small amplitude are constructed for the Vlasov-Poisson system with certain generalized Landau collision operator. The construction of global solution is based on an energy method.
1Villani C., A survey of mathematical topics in kinetic theory, To apear in Handbook of Fluid Mechanics, S. Friedlander and D. Serre, Eds.
2Guo Y., The Landau equation in periodic box, Comm. Math. Phys., 231(2002), 391-434.
3Glassey R., The Cauchy Problem in Kinetic Theory, Philadelphia, PA: SIAM, 1996.
4Degond P., Lemou M., Dispersion relations for the linearized Fokker-Planck equation,Arch. Rat. Mech. Anal., 138(2)(1989), 137-167.
5Diperna, R. J., Lions P. L., Giob'al weak solution of Vlasov-Maxwell systems, Comm. Pure Appl. Math., 6(1989), 729-757.
6Desvillettes L., Villani C., On the spatially homogeneous Landau equation for hard potentials Ⅰ, Comm. P.D.E., 25(1-2)(2000), 179-259.
7Desvillettes L., Villani C., On the spatially homogeneous Landau equation for hard potentials Ⅱ, Comm. P.D.E., 25(1-2)(2000), 261-298.
8Villani C., On a new class of weak solutions to the spatial homogeneous Boltzmann and Landau equations, Arch. Rat. Mech. Anal., 143(3)(1998), 237-307.
9Villani C., On the Landau equation: Weak stability, global existence, Adv. Diff. Eq.,1(5)(1996), 793-816.
10Guo Y., The Vlasov-Poisson-Boltzmann system near Maxwellians, Comm. Pure Appl.Math., 9(2002), 1104-1135.
