Asymptotic behavior of 3-D evolutionary model of Magnetoelasticity for small data
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910343011237888 |
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| author | Hao, Xiaonan Huang, Jiaxi Jiang, Ning Zhao, Lifeng |
| author_facet | Hao, Xiaonan Huang, Jiaxi Jiang, Ning Zhao, Lifeng |
| contents | In this article, we consider the evolutionary model for magnetoelasticity with vanishing viscosity/damping, which is a nonlinear dispersive system. The global regularity and scattering of the evolutionary model for magnetoelasticity under small size of initial data is proved. Our proof relies on the idea of vector-field method due to the quasilinearity and the presence of convective term. A key observation is that we construct a suitable energy functional including the mass quantity, which enable us to provide a good decay estimates for Schrödinger flow. In particular, we establish the asymptotic behavior in both mass and energy spaces for Schrödinger map, not only for gauged equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of 3-D evolutionary model of Magnetoelasticity for small data Hao, Xiaonan Huang, Jiaxi Jiang, Ning Zhao, Lifeng Analysis of PDEs In this article, we consider the evolutionary model for magnetoelasticity with vanishing viscosity/damping, which is a nonlinear dispersive system. The global regularity and scattering of the evolutionary model for magnetoelasticity under small size of initial data is proved. Our proof relies on the idea of vector-field method due to the quasilinearity and the presence of convective term. A key observation is that we construct a suitable energy functional including the mass quantity, which enable us to provide a good decay estimates for Schrödinger flow. In particular, we establish the asymptotic behavior in both mass and energy spaces for Schrödinger map, not only for gauged equation. |
| title | Asymptotic behavior of 3-D evolutionary model of Magnetoelasticity for small data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.11587 |