@article{M2AN_2000__34_3_575_0,
author = {Alexandre, Radjesvarane},
title = {Around {3D} {Boltzmann} non linear operator without angular cutoff, a new formulation},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {575--590},
year = {2000},
publisher = {Dunod},
volume = {34},
number = {3},
mrnumber = {1763526},
zbl = {0952.35167},
language = {en},
url = {https://www.numdam.org/item/M2AN_2000__34_3_575_0/}
}
TY - JOUR AU - Alexandre, Radjesvarane TI - Around 3D Boltzmann non linear operator without angular cutoff, a new formulation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2000 SP - 575 EP - 590 VL - 34 IS - 3 PB - Dunod UR - https://www.numdam.org/item/M2AN_2000__34_3_575_0/ LA - en ID - M2AN_2000__34_3_575_0 ER -
%0 Journal Article %A Alexandre, Radjesvarane %T Around 3D Boltzmann non linear operator without angular cutoff, a new formulation %J ESAIM: Modélisation mathématique et analyse numérique %D 2000 %P 575-590 %V 34 %N 3 %I Dunod %U https://www.numdam.org/item/M2AN_2000__34_3_575_0/ %G en %F M2AN_2000__34_3_575_0
Alexandre, Radjesvarane. Around 3D Boltzmann non linear operator without angular cutoff, a new formulation. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 3, pp. 575-590. https://www.numdam.org/item/M2AN_2000__34_3_575_0/
[1] , Sur l'opérateur de Boltzmann linéaire 3D sans troncature angulaire. Note C. R. Acad. Sci. Paris Sér. I 325 (1997) 959-962. | Zbl | MR
[2] , Remarks on 3D Boltzmann linear equation without cutoff Trans. Theory and Stat. Phys. 28 (1999) 433-473. | Zbl | MR
[3] , Sur l'opérateur de Boltzmann non linéaire 3D sans troncature angulaire. Note C. R. Acad. Sci. Paris Sér. I 326 (1998) 165-168. | Zbl | MR
[4] , Sur le taux de dissipation d'entropie sans troncature angulaire. Note C. R. Acad. Sci. Paris Sér. 7(1998) 311-315. | Zbl | MR
[5] , Une définition des solutions renormalisées pour l'équation de Boltzmann. Note C. R. Acad. Sci. Paris. Sér. I 328 (1999) 987-991. | Zbl | MR
[6] , The linearised Boltzmann operator and applications. In préparation
[7] , Solutions Maxwelliennes pour l'équation de Boltzmann sans troncature angulaire. Note submitted to C. R. Acad. Sci. Paris Sér. I (to appear). | Zbl
[8] , , and , Entropy dissipation and long range interactions. Arch. Rat. Mech. Anal. (to appear). | Zbl | MR
[9] , , On the Boltzmann equation for long-range interactions and the Landau approximation in plasma physics. (Preprints ENS Ulm DMA-99-22, 1999).
[10] , On the Boltzmann equation. Arch. Rat. Mech. Anal. 45 (1972) 1-34. | Zbl | MR
[11] , Intermolecular forces of infinite range and the Boltzmann equation. Arch. Rat. Mech. Anal. 77 (1981) 11-21. | Zbl | MR
[12] , Statistical Mechanics of charged particles. Wiley Interscience, N.Y, USA (1963). | Zbl | MR
[13] , Problèmes Mathématiques dans la Theorie cinétique des Gaz. Almquist and Wiksell, Uppsala (1957). | Zbl | MR
[14] , Mathematical Methods in Kinetic. Theory 2nd Ed Plenum (1990). | Zbl | MR
[15] , , and , The Mathematical Theory of Dilute Gases. Series in Appl. Sci. 106, Springer Verlag, New York (1994). | Zbl | MR
[16] and , 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
[17] , Regularisation properties of the 2D homogeneous Boltzmann equation. Transport Theory Statist. Phys. 26 (1997) 341-357. | Zbl | MR
[18] , Regularisation for the non-cutoff 2D radially symmetric Boltzmann equation. Transport Theory Statist. Phys. 25 (1996) 383-394. | Zbl | MR
[19] , On asymptotics of the Boltzmann equation when the collisions become grazing. Transport Theory Stat. Phys. 21 (1992) 259-276. | Zbl | MR
[20] and , work in préparation.
[21] and , On the Cauchy problem for Boltzmann equation; Global existence and weak stability. Ann. Maths. 130 (1989) 321-366. | Zbl | MR
[22] and , Global weak solutions of kinetic equations. Sem. Mat. Torino 46 (1988) 259-288. | Zbl | MR
[23] , On Boltzmann equations and Fokker-Planck asymptotics. J. Stat. Phys. 89 (1997) 751-776. | Zbl | MR
[24] , Compactness in Boltzmann's equation, via FIO and applic. J. Math. Kyoto Univ. 34 (1994) Part I 391-427, Part II 429-461, Part III 539-584. | Zbl
[25] , On Boltzmann and Landau equations. Phil. Trans. Roy. Soc. London A-346 (1994) 191-204. | Zbl | MR
[26] , Regularity and compactness for Boltzmann collision operators without angular cutoff. Note C. R. Acad. Sci. Paris Sér. I 326 (1998) 37-41. | Zbl | MR
[27] , Boltzmann Collision Operator with Inverse power Intermolecular potentials. C.P.A.M. 27 ( 1974) Part I 407-428; Part II 559-581. | Zbl | MR
[28] , Pseudo-Differenttal Operators. Princeton Univ. Press. (1981).
[29] , Pdo and non linear PDE, Birkhauser, Boston (1991).
[30] , Contributions à l'étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasma, Thèse Université Paris-Dauphine (1998).
[31] , Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off. Rev. Mat. Iberoam (to appear). | Zbl | MR
[32] , Conservative forms of Boltzmann's collision operator: Landau revisited. Math. Mod. Num. An. (1998). | Zbl | Numdam
[33] , Solutions of the Boltzmann equation. In: Patterns and Waves, North-Holland (1985). | Zbl | MR
[34] , Regularity in the Boltzmann equation and the Radon transform. CPDE 19, (1994) 2057-2074. | Zbl | MR






