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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On quadratic derivative Schrödinger equations in one space dimension


Author: Atanas Stefanov
Journal: Trans. Amer. Math. Soc. 359 (2007), 3589-3607
MSC (2000): Primary 35Q55, 35J10
DOI: https://doi.org/10.1090/S0002-9947-07-04207-9
Published electronically: February 23, 2007
MathSciNet review: 2302508
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Abstract: We consider the Schrödinger equation with derivative perturbation terms in one space dimension. For the linear equation, we show that the standard Strichartz estimates hold under specific smallness requirements on the potential. As an application, we establish existence of local solutions for quadratic derivative Schrödinger equations in one space dimension with small and rough Cauchy data.


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Additional Information

Atanas Stefanov
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: stefanov@math.ku.edu

DOI: https://doi.org/10.1090/S0002-9947-07-04207-9
Received by editor(s): February 25, 2005
Published electronically: February 23, 2007
Additional Notes: This research was supported in part by NSF-DMS 0300511.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.