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Relativistic Boltzmann Equation: Large Time Behavior and Finite Speed of Propagation
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2020-12-01 , DOI: 10.1137/20m1332761
Yu-Chu Lin , Ming-Jiea Lyu , Kung-Chien Wu

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5994-6032, January 2020.
In this paper, we deal with the relativistic Boltzmann equation in the whole space ${\mathbb{R}}_{x}^{3}$ under the closed to equilibrium setting. We obtain the existence, uniqueness, and large time behavior of the solution without imposing any Sobolev regularity (both the spatial and velocity variables) on the initial data. Moreover, we recognize the finite speed of propagation of the solution, which reflects the difference, in essence, between the relativistic Boltzmann equation and the classical Boltzmann equation.


中文翻译:

相对论玻尔兹曼方程:大时间行为和有限的传播速度

SIAM数学分析期刊,第52卷,第6期,第5994-6032页,2020
年1月。在本文中,我们处理整个空间$ {\ mathbb {R}} _ {x} ^ {3 } $在接近平衡的设置下。我们获得了解决方案的存在性,唯一性和长时间行为,而没有在初始数据上施加任何Sobolev规律性(空间和速度变量)。此外,我们认识到解的有限传播速度,这从本质上反映了相对论玻耳兹曼方程和经典玻耳兹曼方程之间的差异。
更新日期:2020-12-02
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