On the Landau approximation in plasma physics

 Access to full text

 Full (PDF)

1. [1] Alexandre R, Villani C, On the Boltzmann equation for long range interactions, Comm. Pure Appl. Math.55 (1) (2002) 30-70. Zbl1029.82036MR1857879
2. [2] Alexandre R, Desvillettes L, Villani C, Wennberg B, Entropy dissipation and long-range interactions, Arch. Rational Mech. Anal.152 (4) (2000) 327-355. Zbl0968.76076MR1765272
3. [3] Arsen'ev A, Buryak O, 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. Zbl0724.35090MR1055522
4. [4] Balescu R, Phys. Fluids3 (1960) 52. Zbl0095.43907MR128922
5. [5] Balescu R, Statistical Mechanics of Charged Particles, Wiley Interscience, New York, 1963. Zbl0125.23106MR160579
6. [6] Bogoljubov N, Problems of Dynamical Theory in Statistical Physics, in: de Boer J, Uhlenbeck G.E (Eds.), Studies in Statistical Mechanics, Interscience, New York, 1962. Zbl0116.45101
7. [7] Cercignani C, The Boltzmann Equation and its Applications, Springer, 1988. Zbl0646.76001MR1313028
8. [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. Zbl0924.76002
9. [9] Degond P, Lucquin-Desreux B, The Fokker–Planck asymptotics of the Boltzmann collision operator in the Coulomb case, Math. Models Methods Appl. Sci.2 (2) (1992) 167-182. Zbl0755.35091MR1167768
10. [10] Delcroix J.L, Bers A, Physique des plasmas, 2 volumes, InterEditions/CNRS, 1994, (in French). 
11. [11] Desvillettes L, On asymptotics of the Boltzmann equation when the collisions become grazing, Transp. Theory Stat. Phys.21 (3) (1992) 259-276. Zbl0769.76059MR1165528
12. [12] Desvillettes L, Villani C, On the spatially homogeneous Landau equation with hard potentials. Part II. H-Theorem and applications, Comm. Partial Differential Equations25 (1–2) (2000) 261-298. Zbl0951.35130MR1737548
13. [13] DiPerna R, Lions P.-L, On the Fokker–Planck–Boltzmann equation, Comm. Math. Phys.120 (1988) 1-23. Zbl0671.35068MR972541
14. [14] DiPerna R, Lions P.-L, On the Cauchy problem for the Boltzmann equation: Global existence and weak stability, Ann. Math.130 (1989) 312-366. Zbl0698.45010MR1014927
15. [15] DiPerna R, Lions P.-L, Meyer Y, Lp regularity of velocity averages, Ann. IHP8 (3–4) (1991) 271-287. Zbl0763.35014MR1127927
16. [16] Goudon T, On Boltzmann equations and Fokker–Planck asymptotics: influence of grazing collisions, J. Stat. Phys.89 (3–4) (1997) 751-776. Zbl0918.35136MR1484062
17. [17] Guernsey R.L, The Kinetic theory of fully ionized gases, Off. Nav. Res., Contract1224 (1960) 15. 
18. [18] Y. Guo, The Boltzmann equation for soft potentials, Arch. Ration. Mech. Anal., in press. 
19. [19] Guo Y, The Landau equation in a periodic box, Commun. Math. Phys.231 (2002) 391-434. Zbl1042.76053MR1946444
20. [20] Lifchitz E, Pitaevskii L, Physical Kinetics – Course in Theoretical Physics, vol. 10, Pergamon, Oxford, 1981. 
21. [21] Lenard A, Ann. Phys.3 (1960) 390. 
22. [22] Lions P.-L, Global solutions of kinetic models and related problems, in: Cercignani C, Pulvirenti M (Eds.), Nonequilibrium Problems in Many-Particle Systems, Lecture Notes in Math., vol. 1551, Springer-Verlag, 1992, pp. 58-86. Zbl0799.35184MR1296258
23. [23] Lions P.-L, Compactness in Boltzmann's equation via Fourier integral operators and applications, III, J. Math. Kyoto Univ.34 (3) (1994) 539-584. Zbl0884.35124MR1295942
24. [24] Lions P.-L, On Boltzmann and Landau equations, Phil. Trans. R. Soc. London Ser. A346 (1994) 191-204. Zbl0809.35137MR1278244
25. [25] Lions P.-L, Regularity and compactness for Boltzmann collision operators without angular cut-off, C. R. Acad. Sci. Paris, Sér. I326 (1) (1998) 37-41. Zbl0920.35114MR1649477
26. [26] Rostoker N, Rosenbluth M.N, Phys. Fluids3 (1960) 390. MR113502
27. [27] Schram P, Kinetic Theory of Gases and Plasmas, Kluwer Academic, Dordrecht, 1991. MR1130397
28. [28] Shkarofsky I, Johnston T, Bachynski M, The Particle Kinetics of Plasmas, Addison-Wesley, Reading, MA, 1966. 
29. [29] Villani C, On the Landau equation: weak stability, global existence, Adv. Differential Equations1 (5) (1996) 793-816. Zbl0856.35020MR1392006
30. [30] Villani C, On a new class of weak solutions for the spatially homogeneous Boltzmann and Landau equations, Arch. Rational Mech. Anal.143 (3) (1998) 273-307. Zbl0912.45011MR1650006
31. [31] Villani C, Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off, Rev. Mat. Iberoamericana15 (2) (1999) 335-352. Zbl0934.45010MR1715411
32. [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. [33] Villani C, Conservative forms of Boltzmann's collision operator: Landau revisited, Math. Models Numer. Anal.33 (1) (1999) 209-227. Zbl0919.35140MR1685753
34. [34] Wilhelm H, Momentum and energy exchange between beams of particles interacting by Yukawa-type potentials, Phys. Rev.187 (1) (1969) 382-392. 

1. Laurent Desvillettes, Francesco Salvarani, Characterization of collision kernels
2. Laurent Desvillettes, Francesco Salvarani, Characterization of collision kernels
3. Clément Mouhot, Quelques résultats d’hypocoercitivité en théorie cinétique collisionnelle