标题： 软势能下爱因斯坦-玻尔兹曼方程齐次解的全局存在性 显示英文标题

标题： Future global existence of homogeneous solutions to the Einstein-Boltzmann system with soft potentials

摘要： 我们研究在宇宙学背景下具有软势的爱因斯坦-玻尔兹曼系统的柯西问题。 我们假设 Bianchi I 对称性来描述一个空间齐次但各向异性的宇宙，并考虑宇宙学常数$ \Lambda > 0 $来描述宇宙的加速膨胀。 对于玻尔兹曼方程，我们引入了一个新的权重函数，并应用 Illner 和 Shinbrot 的方法来获得空间齐次小解的未来全局存在性。 对于爱因斯坦方程，我们假设哈勃变量的初始值接近$ ( \Lambda / 3 )^{ 1 / 2 } $。 我们获得了具有软势的爱因斯坦-玻尔兹曼系统空间齐次解的未来全局存在性和渐近行为。 显示英文摘要

摘要： We study the Cauchy problem for the Einstein-Boltzmann system with soft potentials in a cosmological setting. We assume the Bianchi I symmetry to describe a spatially homogeneous, but anisotropic universe and consider a cosmological constant $ \Lambda > 0 $ to describe an accelerated expansion of the universe. For the Boltzmann equation we introduce a new weight function and apply the method of Illner and Shinbrot to obtain the future global existence of spatially homogeneous, small solutions. For the Einstein equations we assume that the initial value of the Hubble variable is close to $ ( \Lambda / 3 )^{ 1 / 2 } $. We obtain the future global existence and asymptotic behavior of spatially homogeneous solutions to the Einstein-Boltzmann system with soft potentials.