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

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

2006-07-03

arxiv.org/abs/math/0607039v2

Mathematics

Analysis of PDEs

30 pages. In the revised version, the following modification was made. (1) A line for dedication was added in the first page.

Scientific paper

10.1007/s00220-007-0337-9

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.

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