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Global Existence and Uniqueness of Solutions to the Maxwell-Schrödinger Equations

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Abstract

The time local and global well-posedness for the Maxwell-Schrödinger equations is considered in Sobolev spaces in three spatial dimensions. The Strichartz estimates of Koch and Tzvetkov type are used for obtaining the solutions in the Sobolev spaces of low regularities. One of the main results is that the solutions exist time globally for large data.

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Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

    Makoto Nakamura

  2. 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.

Additional information

Communicated by P. Constantin

Dedicated to Professor Hiroki Tanabe on his seventy-fifth birthday

Supported by Grant-in-Aid for Young Scientists (B) #16740071 of Japan Ministry of Education, Culture, Sports, Science and Technology.

Supported by Grant-in-Aid for Young Scientists (B) #16740075 of Japan Ministry of Education, Culture, Sports, Science and Technology.

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Nakamura, M., Wada, T. Global Existence and Uniqueness of Solutions to the Maxwell-Schrödinger Equations. Commun. Math. Phys. 276, 315–339 (2007). https://doi.org/10.1007/s00220-007-0337-9

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  • DOI: https://doi.org/10.1007/s00220-007-0337-9

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