Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in 1 and 2 space dimensions
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 19 (1986) no. 4, pp. 519-542.
DOI: 10.24033/asens.1516
Degond, Pierre 1

1 MIP, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France.
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     title = {Global existence of smooth solutions for the {Vlasov-Fokker-Planck} equation in $1$ and $2$ space dimensions},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
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Degond, Pierre. Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 19 (1986) no. 4, pp. 519-542. doi : 10.24033/asens.1516. http://archive.numdam.org/articles/10.24033/asens.1516/

[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] M. S. Baquendi and P. Grisvard, Sur une équation d'évolution changeant de type (J. of functional analysis, 1968, pp. 352-367). | MR | Zbl

[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. | EuDML | Numdam | MR | Zbl

[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. | Zbl

[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. | Zbl

[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. | Zbl

[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). | MR | Zbl

[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). | MR | Zbl

[9] S. V. Iordanskii, The Cauchy problem for the kinetic equation of Plasma (Amer. Math. Soc. Trans., Vol. 2-35, 1964, pp. 351-363). | Zbl

[10] J. L. Lions, Equations différentielles opérationnelles et problèmes aux limites, Springer, Berlin, 1961. | Zbl

[11] H. Neunzert, M. Pulvirenti and L. Triolo, On the Vlasov-Fokker-Planck equation, preprint n° 77, Fachbereich Mathematik, Universitöt Kaiserlautern, January 1984. | MR

[12] L. Tartar, Topics is nonlinear analysis, Publications mathématiques de l'Université de Paris-Sud (Orsay), novembre 1978. | Zbl

[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). | MR | Zbl

[14] S. Wollman, Existence and uniqueness theory of the Vlasov equation, Internal report, Courant Institute, New York, October 1982.

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