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Well-posedness for nonlinear dispersive equations

  • Herbert Koch
  • Daniel Tataru
  • Monica Vişan
Chapter
Part of the Oberwolfach Seminars book series (OWS, volume 45)

Abstract

In this section we will study local and global well-posedness for a number of different equations where the techniques developed so far are relevant. The first example describes the interaction of three waves of different velocities. It is elementary and displays the role of adapted function spaces on an elementary level. The limitations of our current understanding become obvious as well: The result should remain true under small perturbations of the system, but I have no idea how to approach perturbed equations.

Keywords

Fourier Multiplier Strichartz Estimate Unique Weak Solution Bilinear Estimate Nonlinear Dispersive Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Herbert Koch
    • 1
  • Daniel Tataru
    • 2
  • Monica Vişan
    • 3
  1. 1.Institute of MathematicsUniversity of BonnBonnGermany
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  3. 3.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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