论文标题
小的诺德森汇率与稀疏波的收敛速率用于Landau方程
Small Knudsen rate of convergence to rarefaction wave for the Landau equation
论文作者
论文摘要
在本文中，我们关注的是，随着Knudsen Number $ε> 0 $的消失，对具有库仑电位的可压缩欧拉系统的稀疏器的流体动力极限。确切地说，每当$ε> 0 $很小时，对于Landau方程式上的Cauchy问题时，适当的初始数据涉及[\ frac {2} {3}，1] $中的缩放参数$ a \，我们构建了围绕当地的Maxwellian周围的液体数量的唯一全球全局统一统一的解决方案。同时，我们以$ t = 0 $均匀地从$ t = 0 $统一地建立了解决方案的融合，以$ε^{\ frac {\ frac {3} {5} {5} {5} - \ frac {2} {2} {5} {5} a} a} | \lnε| $ as $ as $ as $ am \ε\ 0 $。该证明基于在缩放转换$（t，x）\ to（ε^{ - a} t，ε^{ - a} x）$的缩放转换$（t，x）\ to下组合[19]和[32]的精制能量方法。
In this paper, we are concerned with the hydrodynamic limit to rarefaction waves of the compressible Euler system for the Landau equation with Coulomb potentials as the Knudsen number $ε>0$ is vanishing. Precisely, whenever $ε>0$ is small, for the Cauchy problem on the Landau equation with suitable initial data involving a scaling parameter $a\in [\frac{2}{3},1]$, we construct the unique global-in-time uniform-in-$ε$ solution around a local Maxwellian whose fluid quantities are the rarefaction wave of the corresponding Euler system. In the meantime, we establish the convergence of solutions to the Riemann rarefaction wave uniformly away from $t=0$ at a rate $ε^{\frac{3}{5}-\frac{2}{5}a}|\ln ε|$ as $ε\to 0$. The proof is based on the refined energy approach combining [19] and [32] under the scaling transformation $(t,x)\to (ε^{-a}t,ε^{-a}x)$.
