Regularity of the gain term and strong L 1 convergence to equilibrium for the relativistic Boltzmann equation
Regularity of the gain term and strong L 1 convergence to equilibrium for the relativistic Boltzmann equation
复制标题
相对论玻尔兹曼方程的增益项的规律性和强 L 1 收敛到平衡
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
H. Andréasson
中科院分区：
文献类型：
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作者：
H. Andréasson
本文的主要目的是证明相对论碰撞算符的增益项是正则化的。这是P. L.的一个推广。狮子在非相对论情形下的类似结果。正则化定理在动力学理论中有许多应用，本文仅讨论其中的几个。特别地，研究了相对论性Boltzmann方程周期解的渐近行为。我们证明，只要初始数据满足有限能量和熵的物理自然界限，此类解在$L $1 $内强烈收敛于全局Juttner平衡解（有时称为相对论麦克斯韦解）。
The main purpose of the paper is to show that the gain term of the relativistic collision operator is regularizing. This is a generalization of P. L. Lions’ analogous result in the nonrelativistic situation. The regularizing theorem has many applications in kinetic theory, and a few are discussed in this paper. In particular, the asymptotic behaviour of periodic solutions to the relativistic Boltzmann equation is studied. We show that such solutions converge strongly in $L^1 $ to a global Juttner equilibrium solution (sometimes called a relativistic Maxwellian) provided that the initial data satisfy the physically natural bounds of finite energy and entropy.