Around 3D Boltzmann non linear operator without angular cutoff, a new formulation
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 (2000) no. 3, pp. 575-590.
@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: Mathematical Modelling and Numerical Analysis },
     pages = {575--590},
     publisher = {Dunod},
     address = {Paris},
     volume = {34},
     number = {3},
     year = {2000},
     zbl = {0952.35167},
     mrnumber = {1763526},
     language = {en},
     url = {http://archive.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: Mathematical Modelling and Numerical Analysis 
PY  - 2000
SP  - 575
EP  - 590
VL  - 34
IS  - 3
PB  - Dunod
PP  - Paris
UR  - http://archive.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: Mathematical Modelling and Numerical Analysis 
%D 2000
%P 575-590
%V 34
%N 3
%I Dunod
%C Paris
%U http://archive.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: Mathematical Modelling and Numerical Analysis , Volume 34 (2000) no. 3, pp. 575-590. http://archive.numdam.org/item/M2AN_2000__34_3_575_0/

[1] R. Alexandre, Sur l'opérateur de Boltzmann linéaire 3D sans troncature angulaire. Note C. R. Acad. Sci. Paris Sér. I 325 (1997) 959-962. | MR | Zbl

[2] R. Alexandre, Remarks on 3D Boltzmann linear equation without cutoff Trans. Theory and Stat. Phys. 28 (1999) 433-473. | MR | Zbl

[3] R. Alexandre, Sur l'opérateur de Boltzmann non linéaire 3D sans troncature angulaire. Note C. R. Acad. Sci. Paris Sér. I 326 (1998) 165-168. | MR | Zbl

[4] R. Alexandre, Sur le taux de dissipation d'entropie sans troncature angulaire. Note C. R. Acad. Sci. Paris Sér. 7(1998) 311-315. | MR | Zbl

[5] R. Alexandre, Une définition des solutions renormalisées pour l'équation de Boltzmann. Note C. R. Acad. Sci. Paris. Sér. I 328 (1999) 987-991. | MR | Zbl

[6] R. Alexandre, The linearised Boltzmann operator and applications. In préparation

[7] R. Alexandre, Solutions Maxwelliennes pour l'équation de Boltzmann sans troncature angulaire. Note submitted to C. R. Acad. Sci. Paris Sér. I (to appear). | Zbl

[8] R. Alexandre, L. Desvillettes, C. Villani and B. Wennberg, Entropy dissipation and long range interactions. Arch. Rat. Mech. Anal. (to appear). | MR | Zbl

[9] R. Alexandre, C. Villani, On the Boltzmann equation for long-range interactions and the Landau approximation in plasma physics. (Preprints ENS Ulm DMA-99-22, 1999).

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

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

[12] R. Balescu, Statistical Mechanics of charged particles. Wiley Interscience, N.Y, USA (1963). | MR | Zbl

[13] T. Carleman, Problèmes Mathématiques dans la Theorie cinétique des Gaz. Almquist and Wiksell, Uppsala (1957). | MR | Zbl

[14] C. Cercignani, Mathematical Methods in Kinetic. Theory 2nd Ed Plenum (1990). | MR | Zbl

[15] C. Cercignam, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases. Series in Appl. Sci. 106, Springer Verlag, New York (1994). | MR | Zbl

[16] P. Degond and B. Lucquin, The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case. Math. Models Methods Appl. Sci. 2-2 (1992) 167-182. | MR | Zbl

[17] L. Desvillettes, Regularisation properties of the 2D homogeneous Boltzmann equation. Transport Theory Statist. Phys. 26 (1997) 341-357. | MR | Zbl

[18] L. Desvillettes, Regularisation for the non-cutoff 2D radially symmetric Boltzmann equation. Transport Theory Statist. Phys. 25 (1996) 383-394. | MR | Zbl

[19] L. Desvillettes, On asymptotics of the Boltzmann equation when the collisions become grazing. Transport Theory Stat. Phys. 21 (1992) 259-276. | MR | Zbl

[20] L. Desvillettes and B. Wennberg, work in préparation.

[21] R. J. Diperna and P. L. Lions, On the Cauchy problem for Boltzmann equation; Global existence and weak stability. Ann. Maths. 130 (1989) 321-366. | MR | Zbl

[22] R. J. Diperna and P. L. Lions, Global weak solutions of kinetic equations. Sem. Mat. Torino 46 (1988) 259-288. | MR | Zbl

[23] T. Goudon, On Boltzmann equations and Fokker-Planck asymptotics. J. Stat. Phys. 89 (1997) 751-776. | MR | Zbl

[24] P. L. Lions, 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] P. L. Lions, On Boltzmann and Landau equations. Phil. Trans. Roy. Soc. London A-346 (1994) 191-204. | MR | Zbl

[26] P. L. Lions, Regularity and compactness for Boltzmann collision operators without angular cutoff. Note C. R. Acad. Sci. Paris Sér. I 326 (1998) 37-41. | MR | Zbl

[27] Y. P. Pao, Boltzmann Collision Operator with Inverse power Intermolecular potentials. C.P.A.M. 27 ( 1974) Part I 407-428; Part II 559-581. | MR | Zbl

[28] M. E. Taylor, Pseudo-Differenttal Operators. Princeton Univ. Press. (1981).

[29] M. E. Taylor, Pdo and non linear PDE, Birkhauser, Boston (1991).

[30] C. Villani, 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] C. Villani, Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off. Rev. Mat. Iberoam (to appear). | MR | Zbl

[32] C. Villani, Conservative forms of Boltzmann's collision operator: Landau revisited. Math. Mod. Num. An. (1998). | Numdam | Zbl

[33] S. Ukai, Solutions of the Boltzmann equation. In: Patterns and Waves, North-Holland (1985). | MR | Zbl

[34] B. Wennberg, Regularity in the Boltzmann equation and the Radon transform. CPDE 19, (1994) 2057-2074. | MR | Zbl