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Global existence and asymptotic behavior of solutions for the Maxwell-Schrödinger equations in three space dimensions

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Abstract

In this paper we study the global existence and asymptotic behavior of solutions for the Maxwell-Schrödinger equations under the Coulomb gauge condition in three space dimensions with the final states given att=+∞. This leads to the construction of the modified wave operator for certain scattered data. It is also shown that for the initial data in the range of the modified wave operator, the initial value problem of the Maxwell-Schrödinger equations has the global solutions in time.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Tokyo, 113, Hongo, Tokyo, Japan

    Yoshio Tsutsumi

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  1. Yoshio Tsutsumi
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Communicated by H. Araki

Dedicated to Professor R. Iino on his 70th birthday

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Tsutsumi, Y. Global existence and asymptotic behavior of solutions for the Maxwell-Schrödinger equations in three space dimensions. Commun.Math. Phys. 151, 543–576 (1993). https://doi.org/10.1007/BF02097027

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  • DOI: https://doi.org/10.1007/BF02097027

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