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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer-Verlag New York
About this chapter
Cite this chapter
Linares, F., Ponce, G. (2015). The Nonlinear Schrödinger Equation: Local Theory. In: Introduction to Nonlinear Dispersive Equations. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2181-2_5
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2181-2_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2180-5
Online ISBN: 978-1-4939-2181-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)