In this work, we provide a result on the derivation of the incompressible Navier-Stokes-Fourier system from the Landau equation for hard, Maxwellian and moderately soft potentials. To this end, we first investigate the Cauchy theory associated to the rescaled Landau equation for small initial data. Our approach is based on proving estimates of some adapted Sobolev norms of the solution that are uniform in the Knudsen number. These uniform estimates also allow us to obtain a result of weak convergence towards the fluid limit system.

中文翻译：

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Landau 方程中的不可压缩 Navier-Stokes-Fourier 极限

在这项工作中，我们提供了关于从硬势、麦克斯韦势和中等软势的朗道方程推导不可压缩 Navier-Stokes-Fourier 系统的结果。为此，我们首先研究与小初始数据重新缩放的朗道方程相关的柯西理论。我们的方法基于证明在 Knudsen 数中是一致的解决方案的一些适应 Sobolev 范数的估计。这些统一的估计也使我们能够获得对流体极限系统的弱收敛的结果。