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Local well-posedness for the Maxwell-Schrödinger equation

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Abstract

Time local well-posedness for the Maxwell-Schrödinger equation in the Coulomb gauge is studied in Sobolev spaces by the contraction mapping principle. The Lorentz gauge and the temporal gauge cases are also treated by the gauge transform.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

    Makoto Nakamura

  2. Department of Mathematics, Osaka University, Osaka, 560-0043, Japan

    Takeshi Wada

  3. Department of Mathematics, Faculty of Engineering, Kumamoto University, Kumamoto, 860-8555, Japan

    Takeshi Wada

Authors
  1. Makoto Nakamura
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  2. Takeshi Wada
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Correspondence to Makoto Nakamura.

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Nakamura, M., Wada, T. Local well-posedness for the Maxwell-Schrödinger equation. Math. Ann. 332, 565–604 (2005). https://doi.org/10.1007/s00208-005-0637-3

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  • DOI: https://doi.org/10.1007/s00208-005-0637-3

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