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 \(\varepsilon >0\) is vanishing. Precisely, whenever \(\varepsilon >0\) 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-\(\varepsilon \) 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 \(\varepsilon ^{\frac{3}{5}-\frac{2}{5}a}|\ln \varepsilon |\) as \(\varepsilon \rightarrow 0\). The proof is based on the refined energy approach combining Guo (Commun Math Phys 231:391–434, 2002) and Liu et al. (Physica D 188:178–192, 2004) under the scaling transformation \((t,x)\rightarrow (\varepsilon ^{-a}t,\varepsilon ^{-a}x)\).

在本文中，当Knudsen数\（\ varepsilon> 0 \）消失时，我们关注具有Coulomb势的Landau方程的可压缩Euler系统对稀疏波的流体力学极限。精确地，每当\（\ varepsilon> 0 \）很小时，对于Landau方程上的柯西问题，带有适合的初始数据且涉及缩放参数\（a \ in [\ frac {2} {3}，1] \），我们围绕局部麦克斯韦方程组构造唯一的全局时间均匀分布在（\ varepsilon \）解中，该方程的流体量是相应的Euler系统的稀疏波。在此期间，我们建立与黎曼稀疏波解的收敛从均匀地远离\（T = 0 \）的速率\（\ varepsilon ^ {\ frac {3} {5}-\ frac {2} {5} a} | \ ln \ varepsilon | \）为\（\ varepsilon \ rightarrow 0 \）。证明是基于结合郭（Commun Math Phys 231：391–434，2002）和Liu等人的精炼能源方法。（Physica D 188：178–192，2004）在缩放变换\（（t，x）\ rightarrow（\ varepsilon ^ { -a } t，\ varepsilon ^ {-a} x）\下）。