Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.15708 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908428447776768 |
|---|---|
| author | Xu, Fan Liu, Bin |
| author_facet | Xu, Fan Liu, Bin |
| contents | This paper establishes the global well-posedness of the Landau-Lifshitz-Baryakhtar (LLBar) equation in the whole space $\mathbb{R}^3$. The study first demonstrates the existence and uniqueness of global strong solutions using the weak compactness approach. Furthermore, the existence and uniqueness of classical solutions, as well as arbitrary smooth solutions, are derived through a bootstrap argument. The proofs for the existence of these three types of global solutions are based on Friedrichs mollifier approximation and energy estimates, with the structure of the LLBar equation playing a crucial role in the derivation of the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15708 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness for the Landau-Lifshitz-Baryakhtar equation in $\mathbb{R}^3$ Xu, Fan Liu, Bin Analysis of PDEs This paper establishes the global well-posedness of the Landau-Lifshitz-Baryakhtar (LLBar) equation in the whole space $\mathbb{R}^3$. The study first demonstrates the existence and uniqueness of global strong solutions using the weak compactness approach. Furthermore, the existence and uniqueness of classical solutions, as well as arbitrary smooth solutions, are derived through a bootstrap argument. The proofs for the existence of these three types of global solutions are based on Friedrichs mollifier approximation and energy estimates, with the structure of the LLBar equation playing a crucial role in the derivation of the results. |
| title | Global well-posedness for the Landau-Lifshitz-Baryakhtar equation in $\mathbb{R}^3$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.15708 |