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Global Wellposedness in the Energy Space for the Maxwell-Schrödinger System

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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.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Ioan Bejenaru

  2. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Daniel Tataru

Authors
  1. Ioan Bejenaru
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  2. Daniel Tataru
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Correspondence to Ioan Bejenaru.

Additional information

Communicated by P. Constantin

The first author was partially supported by NSF grant DMS0738442.

The second author was partially supported by NSF grant DMS0354539.

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Bejenaru, I., Tataru, D. Global Wellposedness in the Energy Space for the Maxwell-Schrödinger System. Commun. Math. Phys. 288, 145–198 (2009). https://doi.org/10.1007/s00220-009-0765-9

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  • DOI: https://doi.org/10.1007/s00220-009-0765-9

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