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  3. Defocusing Nonlinear Schrödinger Equations
  • Cited by 14
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2019
      March 2019
      ISBN:
      9781108590518
      9781108472081
      DOI:
      https://doi.org/10.1017/9781108590518
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.48kg, 254 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
      Series:
      Cambridge Tracts in Mathematics (217)
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    Subjects:
    Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
    Series:
    Cambridge Tracts in Mathematics (217)
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    Book description

    This study of Schrödinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations. It presents important proofs, using tools from harmonic analysis, microlocal analysis, functional analysis, and topology. This includes a new proof of Keel–Tao endpoint Strichartz estimates, and a new proof of Bourgain's result for radial, energy-critical NLS. It also provides a detailed presentation of scattering results for energy-critical and mass-critical equations. This book is suitable as the basis for a one-semester course, and serves as a useful introduction to nonlinear Schrödinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.

    Reviews

    ‘This book is an excellent introduction to the energy-critical and mass critical problems and is recommended to researchers and graduate students as a guide to advanced methods in nonlinear partial differential equations.’

    Tohru Ozawa Source: MathSciNet

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