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arXiv · 2405.10342

Diffusive Limit of the Vlasov-Maxwell-Boltzmann System without Angular Cutoff

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

Diffusive limit of the non-cutoff Vlasov-Maxwell-Boltzmann system in perturbation framework still remains open. By employing a new weight function and making full use of the anisotropic dissipation property of the non-cutoff linearized Boltzmann operator, we solve this problem with some novel treatments for non-cutoff potentials $\gamma > \max\{-3, -\frac{3}{2}-2s\}$, including both strong angular singularity $\frac{1}{2} \leq s <1$ and weak angular singularity $0 < s < \frac{1}{2}$. 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 non-cutoff Vlasov-Maxwell-Boltzmann system as well as hydrodynamic limit to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law. The indicators $\gamma > \max\{-3, -\frac{3}{2}-2s\}$ and $0 < s <1$ in this paper cover all ranges that can be achieved by the previously established global solutions to the non-cutoff Vlasov-Maxwell-Boltzmann system in perturbation framework.

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Yuan Xu, Fujun Zhou, Weihua Gong, Weijun Wu. 2024-05-15. Diffusive Limit of the Vlasov-Maxwell-Boltzmann System without Angular Cutoff. https://arxiv.org/abs/2405.10342

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