Maxwell-Schrödinger equations in singular electromagnetic field

Qihong Shi; Yaqian Jia; Jianwei Yang

Applications of Mathematics (2024)

  • Volume: 69, Issue: 4, page 437-450
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Shi, Qihong, Jia, Yaqian, and Yang, Jianwei. "Maxwell-Schrödinger equations in singular electromagnetic field." Applications of Mathematics 69.4 (2024): 437-450. <http://eudml.org/doc/299591>.

@article{Shi2024,
abstract = {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.},
author = {Shi, Qihong, Jia, Yaqian, Yang, Jianwei},
journal = {Applications of Mathematics},
keywords = {MS system; global solvability; energy space; Lorenz gauge},
language = {eng},
number = {4},
pages = {437-450},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Maxwell-Schrödinger equations in singular electromagnetic field},
url = {http://eudml.org/doc/299591},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Shi, Qihong
AU - Jia, Yaqian
AU - Yang, Jianwei
TI - Maxwell-Schrödinger equations in singular electromagnetic field
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 437
EP - 450
AB - 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.
LA - eng
KW - MS system; global solvability; energy space; Lorenz gauge
UR - http://eudml.org/doc/299591
ER -

References

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