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arXiv · 1910.05890

Hydrodynamic limit of the Boltzmann equation to the planar rarefaction wave in three dimensional space

Guanfa Wang·Yong Wang·Jiawei Zhou
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Abstract

In this paper, we establish the global in time hydrodynamic limit of Boltzmann equation to the planar rarefaction wave of compressible Euler system in three dimensional space $x\in\mathbb{R}^3$ for general collision kernels. Our approch is based on a generalized Hilbert expansion, and a recent $L^2-L^\infty$ framework. In particular, we improve the $L^2$-estimate to be a localized version because the planar rarefaction wave is indeed a one-dimensional wave which makes the source terms to be not integrable in the $L^2$ energy estimate of three dimensional problem. We also point out that the wave strength of rarefaction may be large.

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Guanfa Wang, Yong Wang, Jiawei Zhou. 2019-10-14. Hydrodynamic limit of the Boltzmann equation to the planar rarefaction wave in three dimensional space. https://arxiv.org/abs/1910.05890

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