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arXiv · 2402.11587

Asymptotic behavior of 3-D evolutionary model of Magnetoelasticity for small data

Xiaonan Hao·Jiaxi Huang·Ning Jiang·Lifeng Zhao
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Abstract

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 Schr\"odinger flow. In particular, we establish the asymptotic behavior in both mass and energy spaces for Schr\"odinger map, not only for gauged equation.

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Xiaonan Hao, Jiaxi Huang, Ning Jiang, Lifeng Zhao. 2024-02-18. Asymptotic behavior of 3-D evolutionary model of Magnetoelasticity for small data. https://arxiv.org/abs/2402.11587

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