Cauchy problem for the nonlinear Schrödinger equation coupled with the Maxwell equation
Colin, Mathieu1; Watanabe, Tatsuya2
1 University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400, Talence, France INRIA, IMB, UMR 5251, F-33400, Talence, France
2 Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto-City, 603-8555, Japan
Annales Henri Lebesgue, Volume 3 (2020), pp. 67-85.

In this paper, we study the nonlinear Schrödinger equation coupled with the Maxwell equation. Using energy methods, we obtain a local existence result for the Cauchy problem.

Dans cet article, nous nous intéressons au couplage entre une équation de Schrödinger nonlinéaire et les équations de Maxwell. En utilisant des méthodes d’énergie, nous montrons que le problème de Cauchy est localement bien posé.

Received:
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Published online:
DOI: 10.5802/ahl.27
Classification: 35L45, 35Q60, 35L70
Keywords: Schrödinger–Maxwell system, Cauchy problem, symmetric hyperbolic system, energy method
Colin, Mathieu 1; Watanabe, Tatsuya 2

1 University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400, Talence, France INRIA, IMB, UMR 5251, F-33400, Talence, France
2 Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto-City, 603-8555, Japan 
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     title = {Cauchy problem for the nonlinear {Schr\"odinger} equation coupled with the {Maxwell} equation},
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Colin, Mathieu; Watanabe, Tatsuya. Cauchy problem for the nonlinear Schrödinger equation coupled with the Maxwell equation. Annales Henri Lebesgue, Volume 3 (2020), pp. 67-85. doi : 10.5802/ahl.27. http://archive.numdam.org/articles/10.5802/ahl.27/

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