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Structural Resolvent Estimates and Derivative Nonlinear Schrödinger Equations

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Abstract

A refinement of a uniform resolvent estimate is given and several smoothing estimates for Schrödinger equations in the critical case are induced from it. The relation between this resolvent estimate and a radiation condition is discussed. As an application of critical smoothing estimates, we show a global existence result for derivative nonlinear Schrödinger equations.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, UK

    Michael Ruzhansky

  2. Graduate School of Mathematics, Nagoya University Furocho, Chikusa-ku Nagoya, 464-8602, Japan

    Mitsuru Sugimoto

Authors
  1. Michael Ruzhansky
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  2. Mitsuru Sugimoto
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Corresponding author

Correspondence to Michael Ruzhansky.

Additional information

Communicated by P. Constantin

The first author was supported by the EPSRC Leadership Fellowship EP/G007233/1.

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Ruzhansky, M., Sugimoto, M. Structural Resolvent Estimates and Derivative Nonlinear Schrödinger Equations. Commun. Math. Phys. 314, 281–304 (2012). https://doi.org/10.1007/s00220-012-1524-x

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  • DOI: https://doi.org/10.1007/s00220-012-1524-x

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