Hypocoercivity of the relativistic Boltzmann and Landau equations in the whole space
Hypocoercivity of the relativistic Boltzmann and Landau equations in the whole space
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DOI：
10.1016/j.jde.2009.11.027
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发表时间：
2010-03
影响因子：
2.4
通讯作者：
Tong Yang;Hongjun Yu
中科院分区：
文献类型：
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作者：
Tong Yang;Hongjun Yu
研究了一类动力学方程在全空间中的次凸性，得到了平衡态解在函数空间中的最优收敛速度。分析依赖于基本能量方法和补偿函数Kawashima引入到经典玻尔兹曼方程，并由Alfressey和Strauss在相对论环境中发展。它也受到最近工作的启发（Duan et al.，2008 [8]）通过结合谱分析和能量方法对玻尔兹曼方程进行了研究。本文介绍的方法的优点是它可以应用于一些复杂的系统，其详细的光谱是未知的。实际上，只需要通过傅立叶变换对保守输运算子和线性化算子在与碰撞不变量正交的子空间上的耗散进行一些估计。
We study the hypocoercivity property for some kinetic equations in the whole space and obtain the optimal convergence rates of solutions to the equilibrium state in some function spaces. The analysis relies on the basic energy method and the compensating function introduced by Kawashima to the classical Boltzmann equation and developed by Glassey and Strauss in the relativistic setting. It is also motivated by the recent work (Duan et al., 2008 [8]) on the Boltzmann equation by combining the spectrum analysis and energy method. The advantage of the method introduced in this paper is that it can be applied to some complicated system whose detailed spectrum is not known. In fact, only some estimates through the Fourier transform on the conservative transport operator and the dissipation of the linearized operator on the subspace orthogonal to the collision invariants are needed.