Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions

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1. [1] A. A. ARSENEV, Global existence of a weak solution of Vlasov's system of equations (USSR comput. Math. and Math. Phys., Vol. 15, 1975, pp. 131-143). 
2. [2] M. S. BAQUENDI and P. GRISVARD, Sur une équation d'évolution changeant de type (J. of functional analysis, 1968, pp. 352-367). Zbl0164.12701MR40 #6034
3. [3] C. BARDOS and P. DEGOND, Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data to appear in Ann. Inst. Henri-Poincaré ; Analyse non linéaire, Vol. 2, No. 2, 1985, pp. 101-118. Zbl0593.35076MR86k:35129
4. [4] J. T. BEALE, T. KATO and A. MAJDA, Remarks on the breakdown of smooth solutions for the 3.D Euler equations, Preprint, university of Berkeley. Zbl0573.76029
5. [5] P. DEGOND, Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity, Internal Report No. 117, Centre de Mathématiques appliquées, Ecole Polytechnique, Paris. Zbl0619.35088
6. [6] P. DEGOND and S. GALLIC, Existence of solutions and diffusion approximation for a model Fokker-Planck equation of a monoenergetic plasma, Manuscript to appear in internal reports, Ecole Polytechnique. 
7. [7] E. HORST, On the classical solutions of the initial value problem for the unmodified nonlinear Vlasov equation (Math. meth. in the appl. Sci, Vol. 3, 1981, pp. 229-248). Zbl0463.35071MR83h:35110
8. [8] R. ILLNER and H. NEUNZERT, An existence theorem for the unmodified Vlasov equation (Math. meth. in the appl. Sci., Vol. 1, 1979, pp. 530-554). Zbl0415.35076MR80j:35085
9. [9] S. V. IORDANSKII, The Cauchy problem for the kinetic equation of Plasma (Amer. Math. Soc. Trans., Vol. 2-35, 1964, pp. 351-363). Zbl0127.21902
10. [10] J. L. LIONS, Equations différentielles opérationnelles et problèmes aux limites, Springer, Berlin, 1961. Zbl0098.31101
11. [11] H. NEUNZERT, M. PULVIRENTI and L. TRIOLO, On the Vlasov-Fokker-Planck equation, preprint n° 77, Fachbereich Mathematik, Universitöt Kaiserlautern, January 1984. Zbl0561.35070MR86d:82026
12. [12] L. TARTAR, Topics is nonlinear analysis, Publications mathématiques de l'Université de Paris-Sud (Orsay), novembre 1978. Zbl0395.00008
13. [13] S. UKAI and T. OKABE, On the classical solution in the large in time of the two dimensional Vlasov equation (Osaka J. of math., Vol. 15, 1978, pp. 245-261). Zbl0405.35002MR81i:35007
14. [14] S. WOLLMAN, Existence and uniqueness theory of the Vlasov equation, Internal report, Courant Institute, New York, October 1982. 

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