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The Nonlinear Schrödinger Equation: Local Theory

Chapter
Part of the Universitext book series (UTX)

Abstract

In this chapter, we shall study local well-posedness of the nonlinear initial value problem (IVP) associated to the Schrödinger equation. We discuss results for data in \(L^2(\mathbb{R}^n)\), \(H^1(\mathbb{R}^n)\), and other well-posedness issues. We end the chapter with some remarks and comments regarding the issues discussed in the previous sections.

Keywords

Solitary Wave Critical Case Initial Value Problem Strichartz Estimate Subcritical Case 
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.

Copyright information

© Springer-Verlag New York 2015

Authors and Affiliations

  1. 1.Instituto Nacional de Matemática Pura e Aplicada (IMPA)Rio de JaneiroBrazil
  2. 2.Dept. MathematicsUniversity of California, Santa Barbara College of Letters & ScienceSanta BarbaraUSA

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