Renormalization for the Laplacian and global well-possness of the Landau–Lifshitz–Gilbert equation in dimensions n ≥ 3 $n \geq3$
Abstract The global solution of the n ≥ 3 $n \geq3$ Landau–Lifshitz–Gilbert equation on S 2 $\mathbb{S}^{2}$ is studied under the cylindrical symmetric coordinates. An equivalent complex-valued equation in cylindrical symmetric coordinates is obtained by the Hasimoto transformation. A renormalizatio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-05-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-020-01377-6 |
| Summary: | Abstract The global solution of the n ≥ 3 $n \geq3$ Landau–Lifshitz–Gilbert equation on S 2 $\mathbb{S}^{2}$ is studied under the cylindrical symmetric coordinates. An equivalent complex-valued equation in cylindrical symmetric coordinates is obtained by the Hasimoto transformation. A renormalization for the Laplacian is used to transform this equivalent system to a Ginzberg–Landau type system in which the Strichartz estimate can be applied. The global H 2 $H^{2}$ well-posedness of the Cauchy problem for the Landau–Lifshitz–Gilbert equation is established. |
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| ISSN: | 1687-2770 |