Convergence and non-convergence phenomena in Euler-Maxwell to MHD transitions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910920254423040 |
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| author | Kim, Dong-ha Kim, Junha Lee, Jihoon |
| author_facet | Kim, Dong-ha Kim, Junha Lee, Jihoon |
| contents | In this work, we investigate the difference estimate for a class of Euler-Maxwell system and those of magnetohydrodynamics (in short, MHD) systems in three dimensions. We decompose the Euler-Maxwell system into three parts, namely the MHD system, auxiliary linear system and error part system. As a result, we obtain the convergence of the velocity of the fluid $u$, electric fields $E$ and magnetic fields $B$ from the Euler-Maxwell system toward the MHD system in $L^{p}_{t}L^{2}_{x}$ as the speed of light $c$ approaches infinity for $p\in[1,\infty]$. We also derived non-convergence results of electric current $j$ or $cE$, and these results are classified by a certain threshold for $p$. Finally, we investigate how the $L^2$-energy flow of Euler-Maxwell system evolves as c tends to infinity, leading to the vanishing of Ampère's equation in the Euler-Maxwell system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence and non-convergence phenomena in Euler-Maxwell to MHD transitions Kim, Dong-ha Kim, Junha Lee, Jihoon Analysis of PDEs 35Q35, 35Q60, 76D03, 76W05, 78A25 In this work, we investigate the difference estimate for a class of Euler-Maxwell system and those of magnetohydrodynamics (in short, MHD) systems in three dimensions. We decompose the Euler-Maxwell system into three parts, namely the MHD system, auxiliary linear system and error part system. As a result, we obtain the convergence of the velocity of the fluid $u$, electric fields $E$ and magnetic fields $B$ from the Euler-Maxwell system toward the MHD system in $L^{p}_{t}L^{2}_{x}$ as the speed of light $c$ approaches infinity for $p\in[1,\infty]$. We also derived non-convergence results of electric current $j$ or $cE$, and these results are classified by a certain threshold for $p$. Finally, we investigate how the $L^2$-energy flow of Euler-Maxwell system evolves as c tends to infinity, leading to the vanishing of Ampère's equation in the Euler-Maxwell system. |
| title | Convergence and non-convergence phenomena in Euler-Maxwell to MHD transitions |
| topic | Analysis of PDEs 35Q35, 35Q60, 76D03, 76W05, 78A25 |
| url | https://arxiv.org/abs/2504.18890 |