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arXiv · 2207.00126

Hilbert Expansion for Coulomb Collisional Kinetic Models

Zhimeng Ouyang·Lei Wu·Qinghua Xiao
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Abstract

The relativistic Vlasov-Maxwell-Landau (r-VML) system and the relativistic Landau equation (r-LAN) are fundamental models that describe the dynamics of an electron gas. In this paper, we introduce a novel weighted energy method and establish the validity of the Hilbert expansion for the r-VML system and r-LAN equation. As the Knudsen number shrinks to zero, we rigorously demonstrate the relativistic Euler-Maxwell limit and relativistic Euler limit, respectively. This successfully resolves the long-standing open problem regarding the hydrodynamic limits of Landau-type equations.

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Zhimeng Ouyang, Lei Wu, Qinghua Xiao. 2022-06-30. Hilbert Expansion for Coulomb Collisional Kinetic Models. https://arxiv.org/abs/2207.00126

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