Book Volume 45 2014

Dispersive Equations and Nonlinear Waves

Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps

Authors:

ISBN: 978-3-0348-0735-7 (Print) 978-3-0348-0736-4 (Online)

Table of contents (25 chapters)

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  1. Front Matter

    Pages i-xii

  2. Nonlinear Dispersive Equations

    1. Front Matter

      Pages 1-1

    2. No Access

      Chapter

      Pages 3-3

      Introduction

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      Chapter

      Pages 5-22

      Stationary phase and dispersive estimates

    4. No Access

      Chapter

      Pages 23-39

      Strichartz estimates and small data for the nonlinear Schrödinger equation

    5. No Access

      Chapter

      Pages 41-71

      Functions of bounded p-variation

    6. No Access

      Chapter

      Pages 73-85

      Convolution of measures on hypersurfaces, bilinear estimates, and local smoothing

    7. No Access

      Chapter

      Pages 87-109

      Well-posedness for nonlinear dispersive equations

    8. No Access

      Chapter

      Pages 111-122

      Appendix A: Young’s inequality and interpolation

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      Chapter

      Pages 123-126

      Appendix B: Bessel functions

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      Chapter

      Pages 127-134

      Appendic C: The Fourier transform

    11. Back Matter

      Pages 135-137

  3. Geometric Dispersive Evolutions

    1. Front Matter

      Pages 139-139

    2. No Access

      Chapter

      Pages 141-142

      Introduction

    3. No Access

      Chapter

      Pages 143-150

      Maps into manifolds

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      Chapter

      Pages 151-160

      Geometric pde’s

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      Chapter

      Pages 161-199

      Wave maps

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      Chapter

      Pages 201-218

      Schrödinger maps

    7. Back Matter

      Pages 219-222

  4. Dispersive Equations

    1. Front Matter

      Pages 223-224

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      Chapter

      Pages 225-225

      Notation

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      Chapter

      Pages 227-238

      Dispersive and Strichartz estimates

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      Chapter

      Pages 239-243

      An inverse Strichartz inequality

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      Chapter

      Pages 245-250

      A linear profile decomposition

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      Chapter

      Pages 251-257

      Stability theory for the energy-critical NLS

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      Chapter

      Pages 259-260

      A large data critical problem

    8. Back Matter

      Pages 309-312

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