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The Cauchy Problem for the Maxwell–Schrödinger System with a Power-Type Nonlinearity

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Theory, Numerics and Applications of Hyperbolic Problems I (HYP 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 236))

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Abstract

We discuss some results on the Maxwell–Schrödinger system with a nonlinear power-like potential. We prove the local well-posedness in \(H^2(\mathbb {R}^3)\times H^{3/2}(\mathbb {R}^3)\) and the global existence of finite energy weak solutions. Then we apply these results to the analysis of finite energy weak solutions for Quantum Magnetohydrodynamic systems. Our interest in this problem is motivated by some models arising in quantum plasma dynamics.

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Author information

Authors and Affiliations

  1. Gran Sasso Science Institute, L’Aquila, Italy

    Paolo Antonelli & Michele D’Amico

  2. Gran Sasso Science Institute, Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Pierangelo Marcati

Authors
  1. Paolo Antonelli
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  2. Michele D’Amico
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  3. Pierangelo Marcati
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Corresponding author

Correspondence to Michele D’Amico .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Würzburg University, Würzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Antonelli, P., D’Amico, M., Marcati, P. (2018). The Cauchy Problem for the Maxwell–Schrödinger System with a Power-Type Nonlinearity. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems I. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 236. Springer, Cham. https://doi.org/10.1007/978-3-319-91545-6_6

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