Diffusive Limit of the One-species Vlasov-Maxwell-Boltzmann System for Cutoff Hard Potentials
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913377964523520 |
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| author | Wu, Weijun Zhou, Fujun Gong, Weihua Xu, Yuan |
| author_facet | Wu, Weijun Zhou, Fujun Gong, Weihua Xu, Yuan |
| contents | 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 $0\leq γ\leq 1$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02861 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffusive Limit of the One-species Vlasov-Maxwell-Boltzmann System for Cutoff Hard Potentials Wu, Weijun Zhou, Fujun Gong, Weihua Xu, Yuan Analysis of PDEs 35Q20, 35Q83 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 $0\leq γ\leq 1$. 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. |
| title | Diffusive Limit of the One-species Vlasov-Maxwell-Boltzmann System for Cutoff Hard Potentials |
| topic | Analysis of PDEs 35Q20, 35Q83 |
| url | https://arxiv.org/abs/2406.02861 |