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...
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| Format: | Article |
| Language: | English |
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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 |
| _version_ | 1818537445559369728 |
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| author | Penghong Zhong Fengong Wu Shengxiang Tang |
| author_facet | Penghong Zhong Fengong Wu Shengxiang Tang |
| author_sort | Penghong Zhong |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T18:50:49Z |
| format | Article |
| id | doaj.art-bb5ecb8954be411cb4a2e75f506805ae |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-11T18:50:49Z |
| publishDate | 2020-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-bb5ecb8954be411cb4a2e75f506805ae2022-12-22T00:54:18ZengSpringerOpenBoundary Value Problems1687-27702020-05-012020111810.1186/s13661-020-01377-6Renormalization for the Laplacian and global well-possness of the Landau–Lifshitz–Gilbert equation in dimensions n ≥ 3 $n \geq3$Penghong Zhong0Fengong Wu1Shengxiang Tang2Department of Mathematics, Guangdong University of EducationDepartment of Mathematics, Guangdong University of EducationDepartment of Mathematics, Guangdong University of EducationAbstract 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.http://link.springer.com/article/10.1186/s13661-020-01377-6Landau–Lifshitz equationWell-posednessHasimoto transformation |
| spellingShingle | Penghong Zhong Fengong Wu Shengxiang Tang Renormalization for the Laplacian and global well-possness of the Landau–Lifshitz–Gilbert equation in dimensions n ≥ 3 $n \geq3$ Boundary Value Problems Landau–Lifshitz equation Well-posedness Hasimoto transformation |
| title | Renormalization for the Laplacian and global well-possness of the Landau–Lifshitz–Gilbert equation in dimensions n ≥ 3 $n \geq3$ |
| title_full | Renormalization for the Laplacian and global well-possness of the Landau–Lifshitz–Gilbert equation in dimensions n ≥ 3 $n \geq3$ |
| title_fullStr | Renormalization for the Laplacian and global well-possness of the Landau–Lifshitz–Gilbert equation in dimensions n ≥ 3 $n \geq3$ |
| title_full_unstemmed | Renormalization for the Laplacian and global well-possness of the Landau–Lifshitz–Gilbert equation in dimensions n ≥ 3 $n \geq3$ |
| title_short | Renormalization for the Laplacian and global well-possness of the Landau–Lifshitz–Gilbert equation in dimensions n ≥ 3 $n \geq3$ |
| title_sort | renormalization for the laplacian and global well possness of the landau lifshitz gilbert equation in dimensions n ≥ 3 n geq3 |
| topic | Landau–Lifshitz equation Well-posedness Hasimoto transformation |
| url | http://link.springer.com/article/10.1186/s13661-020-01377-6 |
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