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

2007/12/01 by Ioan Bejenaru, Daniel Tataru, Bejenaru, Ioan +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0712.0098

openalex publication_date 2007/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Maxwell-Schrödinger system in \R³⁺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.

Citations

• Subcritical Lp bounds on spectral clusters for Lipschitz metrics

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• Local well-posedness of the Schrödinger flow into \mathbbS² with natural boundary conditions
• The Maxwell-Pauli Equations
• Local Wellposedness and Global Weak Solutions of the Pauli-Darwin/Poisswell Equations

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