Large time behavior of solutions to the 2D damped wave-type magnetohydrodynamic equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929574650052608 |
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| author | Xie, Yaowei Yu, Huan |
| author_facet | Xie, Yaowei Yu, Huan |
| contents | In this paper, we are concerned with the 2D damped wave-type magnetohydrodynamic system (abbreviated as MHD-wave system). The purpose of this paper is to study the large time behavior of solutions to the MHD-wave system, espesically to investigate the influence of the bad term $γ\partial_{tt}b$ on the large time behavior. Rates of decay are obtained for both the solutions and higher derivatives in different Sobolev spaces with explicit rates of $γ$, which shows that the decay rates closely align with that of the MHD system under the same norm, for any fixed $γ>0$. In this sense, these decay rates are optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01461 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large time behavior of solutions to the 2D damped wave-type magnetohydrodynamic equations Xie, Yaowei Yu, Huan Analysis of PDEs 35Q35, 35B40, 76D03 In this paper, we are concerned with the 2D damped wave-type magnetohydrodynamic system (abbreviated as MHD-wave system). The purpose of this paper is to study the large time behavior of solutions to the MHD-wave system, espesically to investigate the influence of the bad term $γ\partial_{tt}b$ on the large time behavior. Rates of decay are obtained for both the solutions and higher derivatives in different Sobolev spaces with explicit rates of $γ$, which shows that the decay rates closely align with that of the MHD system under the same norm, for any fixed $γ>0$. In this sense, these decay rates are optimal. |
| title | Large time behavior of solutions to the 2D damped wave-type magnetohydrodynamic equations |
| topic | Analysis of PDEs 35Q35, 35B40, 76D03 |
| url | https://arxiv.org/abs/2411.01461 |