On the Boltzmann Equation with Stochastic Kinetic Transport: Global Existence of Renormalized Martingale Solutions

被引:13
作者
Punshon-Smith, Samuel [1 ]
Smith, Scott [2 ]
机构
[1] Univ Maryland, College Pk, MD 20742 USA
[2] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany
关键词
HYDRODYNAMIC FLUCTUATIONS; AVERAGING LEMMAS; EXTERNAL FORCES; NOISE; STABILITY; LIMITS; L-1;
D O I
10.1007/s00205-018-1225-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of renormalized (in the sense of DiPerna/Lions) martingale solutions to the Boltzmann equation for large initial data with finite mass, energy, and entropy. Our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kinetic equations. This study includes a criterion for renormalization, the weak closedness of the solution set, and tightness of velocity averages in .
引用
收藏
页码:627 / 708
页数:82
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