Article
| Title: | Maxwell-Schrödinger equations in singular electromagnetic field (English) |
| Author: | Shi, Qihong |
| Author: | Jia, Yaqian |
| Author: | Yang, Jianwei |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 69 |
| Issue: | 4 |
| Year: | 2024 |
| Pages: | 437-450 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We investigate the Cauchy problem of the one dimensional Maxwell-Schrödinger (MS) system under the Lorenz gauge condition. Different from the classical case, we consider the electromagnetic and electrostatic potentials which are growing at space infinity. More precisely, the electrostatic potential is allowed to grow linearly, while for the electromagnetic potential the growth is sublinear. Based on the energy estimates and the gauge transformation, we prove the global existence and the uniqueness of the weak solutions to this system. (English) |
| Keyword: | MS system |
| Keyword: | global solvability |
| Keyword: | energy space |
| Keyword: | Lorenz gauge |
| MSC: | 35Q40 |
| DOI: | 10.21136/AM.2024.0180-23 |
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| Date available: | 2024-08-27T11:16:01Z |
| Last updated: | 2024-09-02 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152528 |
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