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arXiv:math/0607039 [math.AP]AbstractReferencesReviewsResources

Global Existence and Uniqueness of Solutions to the Maxwell-Schr{ö}dinger Equations

Makoto Nakamura, Takeshi Wada

Published 2006-07-03, updated 2007-04-13Version 2

The time local and global well-posedness for the Maxwell-Schr{\"o}dinger 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.

Comments: 30 pages. In the revised version, the following modification was made. (1) A line for dedication was added in the first page. (2) Some lines were added at the bottom in page 4 and the top in page 5 in the first section to make the description accurate. (3) Some typographical errors were corrected throughout the paper
Categories: math.AP, math-ph, math.MP
Subjects: 35Q40, 35Q55, 35L70
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