The Nonlinear Schrödinger Equation: Local Theory

  • Felipe LinaresEmail author
  • Gustavo Ponce
Part of the Universitext book series (UTX)


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.


Solitary Wave Critical Case Initial Value Problem Strichartz Estimate Subcritical Case 
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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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