Geodesic
Maxwell-Schrödinger equations in singular electromagnetic field
Applications of Mathematics, Tome 69 (2024) no. 4, pp. 437-450

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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.
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.
DOI : 10.21136/AM.2024.0180-23
Classification : 35Q40
Keywords: MS system; global solvability; energy space; Lorenz gauge 
Shi, Qihong; Jia, Yaqian; Yang, Jianwei. Maxwell-Schrödinger equations in singular electromagnetic field. Applications of Mathematics, Tome 69 (2024) no. 4, pp. 437-450. doi: 10.21136/AM.2024.0180-23
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     title = {Maxwell-Schr\"odinger equations in singular electromagnetic field},
     journal = {Applications of Mathematics},
     pages = {437--450},
     year = {2024},
     volume = {69},
     number = {4},
     doi = {10.21136/AM.2024.0180-23},
     mrnumber = {4785692},
     zbl = {07953647},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2024.0180-23/}
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