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 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}
}