AI 中文总结
研究非双线性碰撞动力学方程到纳维 - 斯托克斯 - 傅里叶系统的收敛，调和不同策略的收敛结果，将限于双线性碰撞的抽象方法扩展到如玻尔兹曼 - 费米 - 狄拉克等非双线性模型。
AI 中文摘要
我们考虑碰撞算子不一定是双线性的碰撞动力学方程，并证明在加权索伯列夫空间中定量收敛到纳维 - 斯托克斯 - 傅里叶系统，同时描述初始层。本文旨在调和巴尔多斯 - 戈尔塞 - 莱弗莫尔对于守恒宏观量并耗散熵的抽象动力学方程的条件收敛结果与巴尔多斯 - Ukai 对玻尔兹曼方程发起的谱策略。这项工作将热尔韦 - 洛兹仅限于双线性碰撞（玻尔兹曼、朗道或其他模型的二次近似）的抽象方法扩展到非双线性模型，如玻尔兹曼 - 费米 - 狄拉克方程、BGK方程和非线性福克 - 普朗克方程。
英文摘要
We consider collisional kinetic equations whose collision operator is not necessarily bilinear and prove quantitative convergence to the Navier-Stokes-Fourier system in weighted Sobolev spaces, together with a description of the initial layers. The aim of this paper is to conciliate the conditional convergence result of Bardos-Golse-Levermore for abstract kinetic equations conserving macroscopic quantities and dissipating entropy with the spectral strategy initiated by Bardos-Ukai for the Boltzmann equation. This work extends the abstract approach of Gervais-Lods which was restricted to bilinear collisions (Boltzmann, Landau or quadratic approximation of other models) to non-bilinear models such as the Boltzmann-Fermi-Dirac equation, the BGK equation and the nonlinear Fokker-Planck equation.
