NONCUTOFF BOLTZMANN EQUATION WITH SOFT POTENTIALS IN THE WHOLE SPACE

被引：0

作者：

Carrapatoso, Kleber ^{[1
]}

Gervais, Pierre ^{[2
]}

机构：

[1] Ecole Polytech, Inst Polytech Paris, Ctr Math Laurent Schwartz, F-91128 Palaiseau, France

[2] Univ Torino, Dept Econ Social Sci Appl Math & Stat, Turin, Italy

来源：

PURE AND APPLIED ANALYSIS | 2024年 / 6卷 / 01期

关键词：

Boltzmann equation; noncutoff kernels; soft-potentials; large-time behavior; OPTIMAL TIME DECAY; CLASSICAL-SOLUTIONS; GLOBAL EXISTENCE; ANGULAR CUTOFF; EXPONENTIAL DECAY; CAUCHY-PROBLEM; STABILITY;

D O I：

10.2140/paa.2024.6.253

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence, uniqueness and convergence of global solutions to the Boltzmann equation with noncutoff soft potentials in the whole space when the initial data is a small perturbation of a Maxwellian with polynomial decay in velocity. Our method is based in the decomposition of the desired solution into two parts: one with polynomial decay in velocity satisfying the Boltzmann equation with only a dissipative part of the linearized operator, the other with Gaussian decay in velocity verifying the Boltzmann equation with a coupling term.

引用

页码：253 / 303

页数：54

共 42 条

[1] Entropy dissipation and long-range interactions [J].

Alexandre, R ;

Desvillettes, L ;

Villani, C ;

Wennberg, B .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2000, 152 (04) :327-355

[2] The Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential [J].

Alexandre, R. ;

Morimoto, Y. ;

Ukai, S. ;

Xu, C. -J. ;

Yang, T. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (03) :915-1010

[3] The Boltzmann Equation Without Angular Cutoff in the Whole Space: Qualitative Properties of Solutions [J].

Alexandre, R. ;

Morimoto, Y. ;

Ukai, S. ;

Xu, C. -J. ;

Yang, T. .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 202 (02) :599-661

[4] Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff [J].

Alexandre, R. ;

Morimoto, Y. ;

Ukai, S. ;

Xu, C. -J. ;

Yang, T. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2011, 304 (02) :513-581

[5] THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL [J].

Alexandre, R. ;

Morimoto, Y. ;

Ukai, S. ;

Xu, C-J ;

Yang, T. .

ANALYSIS AND APPLICATIONS, 2011, 9 (02) :113-134

[6] Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff [J].

Alexandre, Radjesvarane ;

Herau, Frederic ;

Li, Wei-Xi .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 126 :1-71

[7] LOCAL EXISTENCE WITH MILD REGULARITY FOR THE BOLTZMANN EQUATION [J].

Alexandre, Radjesvarane ;

Morimoto, Yoshinori ;

Ukai, Seiji ;

Xu, Chao-Jiang ;

Yang, Tong .

[8] Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation [J].

Alexandre, Radjesvarane ;

Morimoto, Yoshinori ;

Ukai, Seiji ;

Xu, Chao-Jiang ;

Yang, Tong .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 198 (01) :39-123

[9] Non-cutoff Boltzmann equation with polynomial decay perturbations [J].

Alonso, Ricardo ;

Morimoto, Yoshinori ;

Sun, Weiran ;

Yang, Tong .

REVISTA MATEMATICA IBEROAMERICANA, 2021, 37 (01) :189-292

[10] From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight [J].

Briant, Marc ;

Merino-Aceituno, Sara ;

Mouhot, Clement .

ANALYSIS AND APPLICATIONS, 2019, 17 (01) :85-116

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