Boltzmann to Landau from the gradient flow perspective

被引：10

作者：

Carrillo, Jose A. ^{[1
]}

Delgadino, Matias G. ^{[2
]}

Wu, Jeremy ^{[1
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2022年 / 219卷

基金：

欧洲研究理事会;

关键词：

Boltzmann equation; Plasma particles; Kinetic theory; Gamma-convergence; Gradient flows; SPATIALLY HOMOGENEOUS BOLTZMANN; GRAZING COLLISIONS; GAMMA-CONVERGENCE; EQUATION; REGULARITY; EVOLUTION; LIMIT;

D O I：

10.1016/j.na.2022.112824

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We revisit the grazing collision limit connecting the Boltzmann equation to the Landau(-Fokker-Planck) equation from their recent reinterpretations as gradient flows. Our results are in the same spirit as the gamma-convergence of gradient flows technique introduced by Sandier and Serfaty [39]; Serfaty [41]. In this setting, the grazing collision limit reduces to showing the lower semi-continuous convergence of the Boltzmann entropy-dissipation to the Landau entropy-dissipation. (C) 2022 The Author(s). Published by Elsevier Ltd.

引用

页数：49

共 43 条

[1] Quasi-static evolution and congested crowd transport [J].

Alexander, Damon ;

Kim, Inwon ;

Yao, Yao .

NONLINEARITY, 2014, 27 (04) :823-858

[2] 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

[3] On the Landau approximation in plasma physics [J].

Alexandre, R ;

Villani, C .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2004, 21 (01) :61-95

[4] On the Boltzmann equation for long-range interactions [J].

Alexandre, R ;

Villani, C .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2002, 55 (01) :30-70

[5]

Ambrosio L., 2008, LECT MATH ETH ZURICH, P334

[6]

ARKERYD L, 1972, ARCH RATION MECH AN, V45, P17

[7]

ARKERYD L, 1972, ARCH RATION MECH AN, V45, P1

[8] Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction [J].

Arnrich, Steffen ;

Mielke, Alexander ;

Peletier, Mark A. ;

Savare, Giuseppe ;

Veneroni, Marco .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2012, 44 (3-4) :419-454

[9]

Arsenev A.A., 1990, Mat. Sb., V181, P435

[10] CONVERGENCE OF THE ONE-DIMENSIONAL CAHN-HILLIARD EQUATION [J].

Bellettini, Giovanni ;

Bertini, Lorenzo ;

Mariani, Mauro ;

Novaga, Matteo .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 44 (05) :3458-3480

← 1 2 3 4 5 →