论文标题
截止玻尔兹曼方程与麦克斯韦附近的多项式扰动
Cutoff Boltzmann equation with polynomial perturbation near Maxwellian
论文作者
论文摘要
在本文中，我们考虑了Maxwellian附近的截止Boltzmann方程，我们证明了全球存在和唯一性的截止玻尔兹曼在多项式加权空间中的临界值\ in（-3，1] $中的所有$γ\。我们的证明是基于新建立的boltzmann方程和半群技术的不平等，通过概括$ l_x^\ infty l_x^\ infty l^1_v \ cap l^\ cap l^\ infty_ infty_ $ l^\ infty_ {x，v} $ norm在某些较小条件下的初始$ l^1_x l^\ infty_v $ norm和熵，以便此初始数据允许大幅度振荡。
In this paper, we consider the cutoff Boltzmann equation near Maxwellian, we proved the global existence and uniqueness for the cutoff Boltzmann equation in polynomial weighted space for all $γ\in (-3, 1]$. We also proved initially polynomial decay for the large velocity in $L^2$ space will induce polynomial decay rate, while initially exponential decay will induce exponential rate for the convergence. Our proof is based on newly established inequalities for the cutoff Boltzmann equation and semigroup techniques. Moreover, by generalizing the $L_x^\infty L^1_v \cap L^\infty_{x, v}$ approach, we prove the global existence and uniqueness of a mild solution to the Boltzmann equation with bounded polynomial weighted $L^\infty_{x, v}$ norm under some small condition on the initial $L^1_x L^\infty_v$ norm and entropy so that this initial data allows large amplitude oscillations.
