Global Existence and Uniqueness of Solutions to the Maxwell-Schrödinger Equations |
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| Authors: | Makoto Nakamura Takeshi Wada |
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| Institution: | (1) Mathematical Institute, Tohoku University, Sendai 980-8578, Japan;(2) Department of Mathematics, Faculty of Engineering, Kumamoto University, Kumamoto 860-8555, Japan |
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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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