About ${L}^{p}$ estimates for the spatially homogeneous Boltzmann equation
Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 2, p. 127-142
@article{AIHPC_2005__22_2_127_0,
author = {Desvillettes, Laurent and Mouhot, Cl\'ement},
title = {About ${L}^{p}$ estimates for the spatially homogeneous Boltzmann equation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {22},
number = {2},
year = {2005},
pages = {127-142},
doi = {10.1016/j.anihpc.2004.03.002},
zbl = {1077.76060},
mrnumber = {2123118},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2005__22_2_127_0}
}

Desvillettes, Laurent; Mouhot, Clément. About ${L}^{p}$ estimates for the spatially homogeneous Boltzmann equation. Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 2, pp. 127-142. doi : 10.1016/j.anihpc.2004.03.002. http://www.numdam.org/item/AIHPC_2005__22_2_127_0/

[1] Alexandre R., Desvillettes L., Villani C., Wennberg B., Entropy dissipation and long range interactions, Arch. Rat. Mech. Anal. 152 (2000) 327-355. | MR 1765272 | Zbl 0968.76076

[2] Alexandre R., Villani C., On the Boltzmann equation for long-range interactions, Comm. Pure Appl. Math. 55 (2002) 30-70. | MR 1857879 | Zbl 1029.82036

[3] Arkeryd L., On the Boltzmann equation, Arch. Rat. Mech. Anal. 45 (1972) 1-34. | MR 339665 | Zbl 0245.76059

[4] Arkeryd L., Intermolecular forces of infinite range and the Boltzmann equation, Arch. Rat. Mech. Anal. 77 (1981) 11-21. | MR 630119 | Zbl 0547.76085

[5] Cercignani C., The Boltzmann Equation and its Applications, Springer, 1988. | MR 1313028 | Zbl 0646.76001

[6] Desvillettes L., Some applications of the method of moments for the homogeneous Boltzmann and Kac equations, Arch. Rat. Mech. Anal. 123 (1993) 387-404. | MR 1233644 | Zbl 0784.76081

[7] Desvillettes L., Villani C., On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, uniqueness and smoothness, Comm. Partial Differential Equations 25 (1/2) (2000) 179-259. | MR 1737547 | Zbl 0946.35109

[8] L. Desvillettes, B. Wennberg, Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff, Comm. Partial Differential Equations, submitted for publication. | MR 2038147 | Zbl 1103.82020

[9] M. Escobedo, P. Laurençot, S. Mischler, On a kinetic equation for coalescing particles, Prépublication Inria, 2003. | MR 2048557

[10] Goudon T., On Boltzmann equations and Fokker-Planck asymptotics: influence of grazing collisions, J. Stat. Phys. 89 (3-4) (1997) 751-776. | MR 1484062 | Zbl 0918.35136

[11] Gustafsson T., ${L}^{p}$-estimates for the nonlinear spatially homogeneous Boltzmann equation, Arch. Rat. Mech. Anal. 92 (1986) 23-57. | MR 816620 | Zbl 0619.76100

[12] Gustafsson T., Global ${L}^{p}$-properties for the spatially homogeneous Boltzmann equation, Arch. Rat. Mech. Anal. 103 (1988) 1-38. | MR 946968 | Zbl 0656.76067

[13] Ikenberry E., Truesdell C., On the pressures and the flux of energy in a gas according to Maxwell's kinetic theory. I, Arch. Rat. Mech. Anal. 5 (1956) 1-54. | MR 75725 | Zbl 0070.23504

[14] Lions P.L., Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II, III, J. Math. Kyoto Univ. 34 (1994) 539-584. | MR 1295942 | Zbl 0884.35124

[15] Lions P.L., Regularity and compactness for Boltzmann collision operators without angular cut-off, C. R. Acad. Sci. Paris Sér. I 326 (1) (1998) 37-41. | MR 1649477 | Zbl 0920.35114

[16] Mischler S., Rodriguez Ricard M., Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions, C. R. Acad. Sci. Paris Sér. I 336 (2003) 407-412. | MR 1979355 | Zbl 1036.35072

[17] Mischler S., Wennberg B., On the spatially homogeneous Boltzmann equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (4) (1999) 467-501. | Numdam | MR 1697562 | Zbl 0946.35075

[18] C. Mouhot, C. Villani, Regularity theory for the homogeneous Boltzmann with angular cut-off, Arch. Rat. Mech. Anal., submitted for publication. | Zbl 1063.76086

[19] Toscani G., Villani C., On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds, J. Statist. Phys. 98 (2000) 1279-1309. | MR 1751701 | Zbl 1034.82032

[20] Toscani G., Villani C., Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas, J. Statist. Phys. 94 (1999) 619-637. | MR 1675367 | Zbl 0958.82044

[21] Villani C., On a new class of weak solutions for the spatially homogeneous Boltzmann and Landau equations, Arch. Rat. Mech. Anal. 143 (1998) 273-307. | MR 1650006 | Zbl 0912.45011

[22] Villani C., Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off, Rev. Mat. Iberoam. 15 (1999) 335-352. | MR 1715411 | Zbl 0934.45010

[23] Wennberg B., On moments and uniqueness for solutions to the space homogeneous Boltzmann equation, Transport Theory Statist. Phys. 23 (1994) 533-539. | MR 1264851 | Zbl 0812.76080

[24] Wennberg B., Entropy dissipation and moment production for the Boltzmann equation, J. Statist. Phys. 86 (5-6) (1997) 1053-1066. | MR 1450762 | Zbl 0935.82035