@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {34}, year = {2000}, pages = {575-590}, mrnumber = {1763526}, zbl = {0952.35167}, language = {en}, url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 575-590. http://gdmltest.u-ga.fr/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. | MR 1485611 | Zbl 0897.76081
,[2] Remarks on 3D Boltzmann linear equation without cutoff Trans. Theory and Stat. Phys. 28 (1999) 433-473. | MR 1705619 | Zbl 0939.35147
,[3] Sur l'opérateur de Boltzmann non linéaire 3D sans troncature angulaire. Note C. R. Acad. Sci. Paris Sér. I 326 (1998) 165-168. | MR 1646952 | Zbl 0913.35138
,[4] Sur le taux de dissipation d'entropie sans troncature angulaire. Note C. R. Acad. Sci. Paris Sér. 7(1998) 311-315. | MR 1648449 | Zbl 0916.76072
,[5] Une définition des solutions renormalisées pour l'équation de Boltzmann. Note C. R. Acad. Sci. Paris. Sér. I 328 (1999) 987-991. | MR 1696193 | Zbl 0931.35128
,[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 0942.35139
,[8] Entropy dissipation and long range interactions. Arch. Rat. Mech. Anal. (to appear). | MR 1765272 | Zbl 0968.76076
, , and ,[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. | MR 339665 | Zbl 0245.76059
,[11] Intermolecular forces of infinite range and the Boltzmann equation. Arch. Rat. Mech. Anal. 77 (1981) 11-21. | MR 630119 | Zbl 0547.76085
,[12] Statistical Mechanics of charged particles. Wiley Interscience, N.Y, USA (1963). | MR 160579 | Zbl 0125.23106
,[13] Problèmes Mathématiques dans la Theorie cinétique des Gaz. Almquist and Wiksell, Uppsala (1957). | MR 98477 | Zbl 0077.23401
,[14] Mathematical Methods in Kinetic. Theory 2nd Ed Plenum (1990). | MR 1069558 | Zbl 0726.76083
,[15] The Mathematical Theory of Dilute Gases. Series in Appl. Sci. 106, Springer Verlag, New York (1994). | MR 1307620 | Zbl 0813.76001
, , and ,[16] The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case. Math. Models Methods Appl. Sci. 2-2 (1992) 167-182. | MR 1167768 | Zbl 0755.35091
and ,[17] Regularisation properties of the 2D homogeneous Boltzmann equation. Transport Theory Statist. Phys. 26 (1997) 341-357. | MR 1475459 | Zbl 0901.76072
,[18] Regularisation for the non-cutoff 2D radially symmetric Boltzmann equation. Transport Theory Statist. Phys. 25 (1996) 383-394. | MR 1407542 | Zbl 0871.76077
,[19] On asymptotics of the Boltzmann equation when the collisions become grazing. Transport Theory Stat. Phys. 21 (1992) 259-276. | MR 1165528 | Zbl 0769.76059
,[20]
and , work in préparation.[21] On the Cauchy problem for Boltzmann equation; Global existence and weak stability. Ann. Maths. 130 (1989) 321-366. | MR 1014927 | Zbl 0698.45010
and ,[22] Global weak solutions of kinetic equations. Sem. Mat. Torino 46 (1988) 259-288. | MR 1101105 | Zbl 0813.35087
and ,[23] On Boltzmann equations and Fokker-Planck asymptotics. J. Stat. Phys. 89 (1997) 751-776. | MR 1484062 | Zbl 0918.35136
,[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 0831.35139
,[25] On Boltzmann and Landau equations. Phil. Trans. Roy. Soc. London A-346 (1994) 191-204. | MR 1278244 | Zbl 0809.35137
,[26] Regularity and compactness for Boltzmann collision operators without angular cutoff. Note C. R. Acad. Sci. Paris Sér. I 326 (1998) 37-41. | MR 1649477 | Zbl 0920.35114
,[27] Boltzmann Collision Operator with Inverse power Intermolecular potentials. C.P.A.M. 27 ( 1974) Part I 407-428; Part II 559-581. | MR 636407 | Zbl 0304.45010
,[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). | MR 1715411 | Zbl 0934.45010
,[32] Conservative forms of Boltzmann's collision operator: Landau revisited. Math. Mod. Num. An. (1998). | Numdam | Zbl 0919.35140
,[33] Solutions of the Boltzmann equation. In: Patterns and Waves, North-Holland (1985). | MR 882376 | Zbl 0633.76078
,[34] Regularity in the Boltzmann equation and the Radon transform. CPDE 19, (1994) 2057-2074. | MR 1301182 | Zbl 0818.35128
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