@article{AIHPC_2004__21_1_61_0,
author = {Alexandre, R and Villani, C},
title = {On the {Landau} approximation in plasma physics},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {61--95},
year = {2004},
publisher = {Elsevier},
volume = {21},
number = {1},
doi = {10.1016/j.anihpc.2002.12.001},
mrnumber = {2037247},
zbl = {1044.83007},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2002.12.001/}
}
TY - JOUR AU - Alexandre, R AU - Villani, C TI - On the Landau approximation in plasma physics JO - Annales de l'I.H.P. Analyse non linéaire PY - 2004 SP - 61 EP - 95 VL - 21 IS - 1 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2002.12.001/ DO - 10.1016/j.anihpc.2002.12.001 LA - en ID - AIHPC_2004__21_1_61_0 ER -
%0 Journal Article %A Alexandre, R %A Villani, C %T On the Landau approximation in plasma physics %J Annales de l'I.H.P. Analyse non linéaire %D 2004 %P 61-95 %V 21 %N 1 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2002.12.001/ %R 10.1016/j.anihpc.2002.12.001 %G en %F AIHPC_2004__21_1_61_0
Alexandre, R; Villani, C. On the Landau approximation in plasma physics. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 1, pp. 61-95. doi: 10.1016/j.anihpc.2002.12.001
[1] , , On the Boltzmann equation for long range interactions, Comm. Pure Appl. Math. 55 (1) (2002) 30-70. | Zbl | MR
[2] , , , , Entropy dissipation and long-range interactions, Arch. Rational Mech. Anal. 152 (4) (2000) 327-355. | Zbl | MR
[3] , , On the connection between a solution of the Boltzmann equation and a solution of the Landau-Fokker-Planck equation, Math. USSR-Sb. 69 (2) (1991) 465-478. | Zbl | MR
[4] , Phys. Fluids 3 (1960) 52. | Zbl | MR
[5] , Statistical Mechanics of Charged Particles, Wiley Interscience, New York, 1963. | Zbl | MR
[6] , Problems of Dynamical Theory in Statistical Physics, in: , (Eds.), Studies in Statistical Mechanics, Interscience, New York, 1962. | Zbl
[7] , The Boltzmann Equation and its Applications, Springer, 1988. | Zbl | MR
[8] A. Decoster, in: Modeling of Collisions, by A. Decoster, P. Markowich and B. Perthame. Gauthier-Villars, Éditions Scientifiques et Médicales Elsevier, Paris, 1998. Edited and with a foreword by P.A. Raviart. | Zbl
[9] , , The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case, Math. Models Methods Appl. Sci. 2 (2) (1992) 167-182. | Zbl | MR
[10] , , Physique des plasmas, 2 volumes, InterEditions/CNRS, 1994, (in French).
[11] , On asymptotics of the Boltzmann equation when the collisions become grazing, Transp. Theory Stat. Phys. 21 (3) (1992) 259-276. | Zbl | MR
[12] , , On the spatially homogeneous Landau equation with hard potentials. Part II. H-Theorem and applications, Comm. Partial Differential Equations 25 (1-2) (2000) 261-298. | Zbl | MR
[13] , , On the Fokker-Planck-Boltzmann equation, Comm. Math. Phys. 120 (1988) 1-23. | Zbl | MR
[14] , , On the Cauchy problem for the Boltzmann equation: Global existence and weak stability, Ann. Math. 130 (1989) 312-366. | Zbl | MR
[15] , , , Lp regularity of velocity averages, Ann. IHP 8 (3-4) (1991) 271-287. | Zbl | MR | Numdam
[16] , On Boltzmann equations and Fokker-Planck asymptotics: influence of grazing collisions, J. Stat. Phys. 89 (3-4) (1997) 751-776. | Zbl | MR
[17] , The Kinetic theory of fully ionized gases, Off. Nav. Res., Contract 1224 (1960) 15.
[18] Y. Guo, The Boltzmann equation for soft potentials, Arch. Ration. Mech. Anal., in press.
[19] , The Landau equation in a periodic box, Commun. Math. Phys. 231 (2002) 391-434. | Zbl | MR
[20] , , Physical Kinetics - Course in Theoretical Physics, vol. 10, Pergamon, Oxford, 1981.
[21] , Ann. Phys. 3 (1960) 390.
[22] , Global solutions of kinetic models and related problems, in: , (Eds.), Nonequilibrium Problems in Many-Particle Systems, Lecture Notes in Math., vol. 1551, Springer-Verlag, 1992, pp. 58-86. | Zbl | MR
[23] , Compactness in Boltzmann's equation via Fourier integral operators and applications, III, J. Math. Kyoto Univ. 34 (3) (1994) 539-584. | Zbl | MR
[24] , On Boltzmann and Landau equations, Phil. Trans. R. Soc. London Ser. A 346 (1994) 191-204. | Zbl | MR
[25] , Regularity and compactness for Boltzmann collision operators without angular cut-off, C. R. Acad. Sci. Paris, Sér. I 326 (1) (1998) 37-41. | Zbl | MR
[26] , , Phys. Fluids 3 (1960) 390. | MR
[27] , Kinetic Theory of Gases and Plasmas, Kluwer Academic, Dordrecht, 1991. | MR
[28] , , , The Particle Kinetics of Plasmas, Addison-Wesley, Reading, MA, 1966.
[29] , On the Landau equation: weak stability, global existence, Adv. Differential Equations 1 (5) (1996) 793-816. | Zbl | MR
[30] , On a new class of weak solutions for the spatially homogeneous Boltzmann and Landau equations, Arch. Rational Mech. Anal. 143 (3) (1998) 273-307. | Zbl | MR
[31] , Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off, Rev. Mat. Iberoamericana 15 (2) (1999) 335-352. | Zbl | MR
[32] C. Villani, Contribution à l'étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasmas, PhD thesis, Univ. Paris-Dauphine, 1998.
[33] , Conservative forms of Boltzmann's collision operator: Landau revisited, Math. Models Numer. Anal. 33 (1) (1999) 209-227. | Zbl | MR | Numdam
[34] , Momentum and energy exchange between beams of particles interacting by Yukawa-type potentials, Phys. Rev. 187 (1) (1969) 382-392.
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