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Energy convergence for singular limits of Zakharov type systems

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Abstract

We prove existence and uniqueness of solutions to the Klein–Gordon–Zakharov system in the energy space H 1×L 2 on some time interval which is uniform with respect to two large parameters c and α. These two parameters correspond to the plasma frequency and the sound speed. In the simultaneous high-frequency and subsonic limit, we recover the nonlinear Schrödinger system at the limit. We are also able to say more when we take the limits separately.

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Authors and Affiliations

  1. Courant Institute, New York University, New York, NY, 10012, USA

    Nader Masmoudi

  2. Department of Mathematics, Kyoto University, 606-8502, Kyoto, Japan

    Kenji Nakanishi

Authors
  1. Nader Masmoudi
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  2. Kenji Nakanishi
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Correspondence to Nader Masmoudi.

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Masmoudi, N., Nakanishi, K. Energy convergence for singular limits of Zakharov type systems. Invent. math. 172, 535–583 (2008). https://doi.org/10.1007/s00222-008-0110-5

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  • DOI: https://doi.org/10.1007/s00222-008-0110-5

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