Global Existence and Uniqueness of Solutions to the   Maxwell-Schr{\"o}dinger Equations
  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. 
Makoto Nakamura, Takeshi Wada