2024/05/15 by Yuan Xu, Fujun Zhou, Xu, Yuan +5
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Phase Equilibria and Thermodynamics
paper · pdf · doi:10.48550/arxiv.2405.10342
openalex publication_date 2024/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 γ> max\-3, -(3)/(2)-2s\, including both strong angular singularity (1)/(2) ≤ s <1 and weak angular singularity 0 < s < (1)/(2). Uniform estimate with respect to the Knudsen number ε∈ (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 γ> max\-3, -(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.