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arXiv · 2406.02861

Diffusive Limit of the One-species Vlasov-Maxwell-Boltzmann System for Cutoff Hard Potentials

Weijun Wu·Fujun Zhou·Weihua Gong·Yuan Xu
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Abstract

Diffusive limit of the one-species Vlasov-Maxwell-Boltzmann system in perturbation framework still remains unsolved, due to the weaker time decay rate compared with the two-species Vlasov-Maxwell-Boltzmann system. By employing the weighted energy method with two newly introduced weight functions and some novel treatments, we solve this problem for the full range of cutoff hard potentials $0\leq \gamma \leq 1$. Uniform estimate with respect to the Knudsen number $\varepsilon\in (0,1]$ is established globally in time, which eventually leads to the global existence of solutions to the one-species Vlasov-Maxwell-Boltzmann system and hydrodynamic limit to the incompressible Navier-Stokes-Fourier-Maxwell system. To the best of our knowledge, this is the first result on diffusive limit of the one-species Vlasov-Maxwell-Boltzmann system in perturbation framework.

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Weijun Wu, Fujun Zhou, Weihua Gong, Yuan Xu. 2024-06-05. Diffusive Limit of the One-species Vlasov-Maxwell-Boltzmann System for Cutoff Hard Potentials. https://arxiv.org/abs/2406.02861

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