ON THE VLASOV-POISSON-FOKKER-PLANCK EQUATION NEAR MAXWELLIAN

被引：38

作者：

Hwang, Hyung Ju ^{[1
]}

Jang, Juhi ^{[2
]}

机构：

[1] Pohang Univ Sci & Technol, Dept Math, Pohang 790784, South Korea

[2] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2013年 / 18卷 / 03期

基金：

美国国家科学基金会; 新加坡国家研究基金会;

关键词：

Vlasov-Poisson-Fokker-Planck; hypocoercivity; exponential time decay rate; energy estimates; macroscopic equations; GLOBAL CLASSICAL-SOLUTIONS; BOLTZMANN-EQUATION; EQUILIBRIUM; SYSTEM; TREND; EXISTENCE;

D O I：

10.3934/dcdsb.2013.18.681

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the exponential time decay rate of smooth solutions of small amplitude to the Vlasov-Poisson-Fokker-Planck equations to the Maxwellian both in the whole space and in the periodic box via the uniform-in-time energy estimates and also the macroscopic equations.

引用

页码：681 / 691

页数：11

共 27 条

[1]

[Anonymous], 1970, SINGULAR INTEGRALS D

[2] EXISTENCE AND UNIQUENESS OF A GLOBAL SMOOTH SOLUTION FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM IN 3 DIMENSIONS [J].

BOUCHUT, F .

JOURNAL OF FUNCTIONAL ANALYSIS, 1993, 111 (01) :239-258

[3] SMOOTHING EFFECT FOR THE NONLINEAR VLASOV-POISSON-FOKKER-PLANCK SYSTEM [J].

BOUCHUT, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 122 (02) :225-238

[4] Hypoelliptic regularity in kinetic equations [J].

Bouchut, F .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2002, 81 (11) :1135-1159

[5]

Bouchut F., 1995, Differential Integral Equations, V8, P487

[6]

Carpio A, 1998, MATH METHOD APPL SCI, V21, P985, DOI 10.1002/(SICI)1099-1476(19980725)21:11<985::AID-MMA919>3.0.CO

[7]

2-B

[8] Asymptotic behaviour and self-similarity for the three dimensional Vlasov-Poisson-Fokker-Planck system [J].

Carrillo, JA ;

Soler, J ;

Vazquez, JL .

JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 141 (01) :99-132

[9] ON THE INITIAL-VALUE PROBLEM FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM WITH INITIAL DATA IN L(P) SPACES [J].

CARRILLO, JA ;

SOLER, J .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1995, 18 (10) :825-839

[10] GLOBAL CLASSICAL SOLUTIONS CLOSE TO EQUILIBRIUM TO THE VLASOV-FOKKER-PLANCK-EULER SYSTEM [J].

Carrillo, Jose A. ;

Duan, Renjun ;

Moussa, Ayman .

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