与辐射相互作用的气体中的LTE和非LTE解决方案
LTE and Non-LTE Solutions in Gases Interacting with Radiation
摘要：
本文研究了一类描述气体中辐射传递的动力学方程，该方程也包含了气体分子之间的相互作用。我们讨论了几个标度限制，并介绍了一些欧拉与辐射耦合的系统作为特定的标度限制的后果。我们考虑局部热力学平衡（LTE）的缩放限制，以及这种假设失败（非LTE）的情况。描述气体辐射系统的方程的结构在LTE和非LTE情况下非常不同。我们证明了零速度的平稳解的存在性，在LTE的情况下，由此产生的极限模型。我们还证明了在非LTE的情况下，零速度的定态的不存在。
英文摘要：
In this paper, we study a class of kinetic equations describing radiative transfer in gases which include also the interaction of the molecules of the gas with themselves. We discuss several scaling limits and introduce some Euler-like systems coupled with radiation as an aftermath of specific scaling limits. We consider scaling limits in which local thermodynamic equilibrium (LTE) holds, as well as situations in which this assumption fails (non-LTE). The structure of the equations describing the gas-radiation system is very different in the LTE and non-LTE cases. We prove the existence of stationary solutions with zero velocities to the resulting limit models in the LTE case. We also prove the non-existence of a stationary state with zero velocities in a non-LTE case.
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