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

Abstract

We prove that the Maxwell-Schrödinger system in ${\mathbb{R}}^{3+1}$ 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.

References in corpus (2)

• A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces
• Subcritical Lp bounds on spectral clusters for Lipschitz metrics