Uncertainty principle and regularity for Boltzmann type equations

Radjesvarane Alexandre; Yoshinori Morimoto; Seiji Ukai; Chao-Jiang Xu; Tong Yang

doi:10.1016/j.crma.2007.10.032

Partial Differential Equations/Harmonic Analysis

Uncertainty principle and regularity for Boltzmann type equations
[Principe d'incertitude et régularité pour des équations de type Boltzmann]

Présenté par : Jean-Michel Bony

Radjesvarane Alexandre ¹ ; Yoshinori Morimoto ² ; Seiji Ukai ³ ; Chao-Jiang Xu ⁴ ; Tong Yang ^3,⁵

¹ IRENAv, French Naval Academy, 29240 Brest-Lanvéoc, France
² Kyoto University, Japan
³ City University, 83, Tat Chee Avenue, Kowloon, Hong Kong
⁴ Université de Rouen, avenue de l'université, technopôle du Madrillet, 76801 Saint Étienne du Rouvray cedex, France
⁵ Shanghai Jiao Tong University, PR China

Comptes Rendus. Mathématique, Volume 345 (2007) no. 12, pp. 673-677.

Résumé
Abstract

Nous montrons une version généralisée du principe d'incertitude, et l'appliquons à l'étude de propriétés de régularisation de solutions d'équations cinétiques. En particulier, nous considérons les versions linéarisée et non linéaire de l'équation de Boltzmann, sans faire l'hypothèse de troncature angulaire de Grad.

We give a generalized version of uncertainty principle, and apply it to the study of regularization properties of solutions to kinetic equations. In particular, both linearized and nonlinear space inhomogeneous Boltzmann equations without Grad's cutoff assumption are considered.

Reçu le : 2007-09-20
Accepté le : 2007-10-16
Publié le : 2007-11-26

DOI : 10.1016/j.crma.2007.10.032

Affiliations des auteurs :

Radjesvarane Alexandre ¹ ; Yoshinori Morimoto ² ; Seiji Ukai ³ ; Chao-Jiang Xu ⁴ ; Tong Yang ^{3, 5}

¹ IRENAv, French Naval Academy, 29240 Brest-Lanvéoc, France
² Kyoto University, Japan
³ City University, 83, Tat Chee Avenue, Kowloon, Hong Kong
⁴ Université de Rouen, avenue de l'université, technopôle du Madrillet, 76801 Saint Étienne du Rouvray cedex, France
⁵ Shanghai Jiao Tong University, PR China

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     title = {Uncertainty principle and regularity for {Boltzmann} type equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {673--677},
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     year = {2007},
     doi = {10.1016/j.crma.2007.10.032},
     language = {en},
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Radjesvarane Alexandre; Yoshinori Morimoto; Seiji Ukai; Chao-Jiang Xu; Tong Yang. Uncertainty principle and regularity for Boltzmann type equations. Comptes Rendus. Mathématique, Volume 345 (2007) no. 12, pp. 673-677. doi : 10.1016/j.crma.2007.10.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.032/

Bibliographie
Cité par

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Zhong Tan; Yanzhen Wang; Shuhong Chen Partial regularity up to the boundary for solutions of subquadratic elliptic systems, Advances in Nonlinear Analysis, Volume 7 (2018) no. 4, p. 469 | DOI:10.1515/anona-2016-0054
R. Alexandre; Y. Morimoto; S. Ukai; C. -J. Xu; T. Yang Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff, Communications in Mathematical Physics, Volume 304 (2011) no. 2, p. 513 | DOI:10.1007/s00220-011-1242-9
Radjesvarane Alexandre; Yoshinori Morimoto; Seiji Ukai; Chao-Jiang Xu; Tong Yang Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation, Archive for Rational Mechanics and Analysis, Volume 198 (2010) no. 1, p. 39 | DOI:10.1007/s00205-010-0290-1
Hua Chen; Wei-Xi Li; Chao-Jiang Xu Gevrey hypoellipticity for linear and non-linear Fokker–Planck equations, Journal of Differential Equations, Volume 246 (2009) no. 1, p. 320 | DOI:10.1016/j.jde.2008.05.019

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