English

Global wellposedness in the energy space for the Maxwell-Schr\"odinger system

Analysis of PDEs 2007-12-04 v1

Abstract

We prove that the Maxwell-Schr\"odinger system in R3+1\R^{3+1} is globally well-posed in the energy space. The key element of the proof is to obtain a short time wave packet parametrix for the magnetic Schr\"odinger equation, which leads to linear, bilinear and trilinear estimates. These, in turn, are extended to larger time scales via a bootstrap argument.

Keywords

Cite

@article{arxiv.0712.0098,
  title  = {Global wellposedness in the energy space for the Maxwell-Schr\"odinger system},
  author = {Ioan Bejenaru and Daniel Tataru},
  journal= {arXiv preprint arXiv:0712.0098},
  year   = {2007}
}