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arXiv · 0712.0098

Global wellposedness in the energy space for the Maxwell-Schrödinger system

Ioan Bejenaru·Daniel Tataru
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Abstract

We prove that the Maxwell-Schrödinger system in $\R^{3+1}$ 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 Schrödinger equation, which leads to linear, bilinear and trilinear estimates. These, in turn, are extended to larger time scales via a bootstrap argument.

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Ioan Bejenaru, Daniel Tataru. 2007-12-01. Global wellposedness in the energy space for the Maxwell-Schrödinger system. https://arxiv.org/abs/0712.0098

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