On the quantum Boltzmann equation near Maxwellian and vacuum
On the quantum Boltzmann equation near Maxwellian and vacuum
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DOI：
10.1016/j.jde.2022.01.056
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发表时间：
2021-02
影响因子：
2.4
通讯作者：
Zhimeng Ouyang;Lei Wu
中科院分区：
文献类型：
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作者：
Zhimeng Ouyang;Lei Wu
我们考虑费米子和玻色子的非相对论量子玻尔兹曼方程。利用非线性能量法和温和公式，证明了密度函数在接近全局麦克斯韦和真空时的全局适定性。这项工作是对经典玻尔兹曼理论的推广和改编。我们的主要贡献是对量子背景下的非线性算子进行了详细的分析。这是一个关于量子动力学方程的长期项目的第一部分。
We consider the non-relativistic quantum Boltzmann equation for fermions and bosons. Using the nonlinear energy method and mild formulation, we justify the global well-posedness when the density function is near the global Maxwellian and vacuum. This work is a generalization and adaptation of the classical Boltzmann theory. Our main contribution is a detailed analysis of the nonlinear operatorQin the quantum context. This is the first piece of a long-term project on the quantum kinetic equations.