标题： 一维BGK模型在可压缩气体动力学中的整体温和解 显示英文标题

标题： Global Mild Solutions to a BGK Model for Barotropic Gas Dynamics

摘要： 我们在有限动能熵初始数据的最小假设下，建立了Bouchut提出的BGK模型的温和解的整体存在性。此外，我们严格推导出一个动能熵不等式，该不等式结合Berthelin和Vasseur发展的理论，导致了到压缩流Euler方程的流体动力学极限。分析中使用的主要工具是麦克斯韦分布的稳定性估计和速度平均引理。 显示英文摘要

摘要： We establish global existence of mild solutions to the BGK model proposed by Bouchut [J. Stat. Phys., 95, (1999), 113--170] under the minimal assumption of finite kinetic entropy initial data. Moreover we rigorously derive a kinetic entropy inequality, which combined with the theory developed by Berthelin and Vasseur [SIAM J. Math. Anal., 36, (2005), 1807--1835] leads to the hydrodynamic limit to the barotropic Euler equations. The main tools employed in the analysis are stability estimates for the Maxwellian and a velocity averaging lemma.