Cauchy problem for the nonlinear Schrödinger equation coupled with the Maxwell equation
[Problème de Cauchy pour une équation de Schrödinger nonlinéaire couplée avec les équations de Maxwell]
Annales Henri Lebesgue, Tome 3 (2020), pp. 67-85.

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.

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.

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DOI : 10.5802/ahl.27
Classification : 35L45, 35Q60, 35L70
Mots clés : 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, Tome 3 (2020), pp. 67-85. doi : 10.5802/ahl.27. http://www.numdam.org/articles/10.5802/ahl.27/

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