Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition

被引：2

作者：

Bernou, Armand ^{[1
]}

Carrapatoso, Kleber ^{[2
]}

Mischler, Stephane ^{[3
]}

Tristani, Isabelle ^{[4
]}

机构：

[1] Sorbonne Univ, Lab Probabilite Stat & Modelisat, 4 Pl Jussieu, F-75005 Paris, France

[2] Ecole Polytech, Inst Polytech Paris, CMLS, F-91128 Palaiseau, France

[3] Univ Paris 09, UMR 7534, CEREMADE, Pl Marechal de Lattre de Tassigny, F-75775 Paris 16, France

[4] PSL Univ, Ecole Normale Super, Dept Math & Applicat, CNRS, F-75005 Paris, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2023年 / 40卷 / 02期

关键词：

Kinetic equations; hypocoercivity; Boltzmann equation; Landau equation; spectral gap; convergence to equilibrium; Poincare inequality; Korn inequality; INCOMPRESSIBLE NAVIER-STOKES; FOKKER-PLANCK EQUATION; FLUID DYNAMIC LIMITS; BOLTZMANN-EQUATION; FOURIER LIMIT; GLOBAL EQUILIBRIUM; EXPONENTIAL DECAY; TRACE THEOREMS; WAVE-EQUATION; SPECTRAL GAP;

D O I：

10.4171/AIHPC/44

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary condition. Our proof consists in establishing an hypocoercivity result for the associated operator; in other words, we exhibit a convenient Hilbert norm for which the associated operator is coercive in the orthogonal of the global conservation laws. Our approach allows us to treat general domains with all types of boundary conditions in a unified framework. In particular, our result includes the case of vanishing accommodation coefficient and thus the specific case of the specular reflection boundary condition.

引用

页码：287 / 338

页数：52

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