Revista Matemática Complutense

, Volume 31, Issue 2, pp 449–465 | Cite as

Local Cauchy theory for the nonlinear Schrödinger equation in spaces of infinite mass

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Abstract

We consider the Cauchy problem for the nonlinear Schrödinger equation on \(\mathbb {R}^d\), where the initial data is in \(\dot{H}^1(\mathbb {R}^d)\cap L^p(\mathbb {R}^d)\). We prove local well-posedness for large ranges of p and discuss some global well-posedness results.

Keywords

Nonlinear Schrödinger equation Local well-posedness Global well-posedness 

Mathematics Subject Classification

35Q55 35A01 
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Notes

Acknowledgements

The author was partially suported by Fundação para a Ciência e Tecnologia, through the Grants UID/MAT/04561/2013 and SFRH/BD/96399/2013.

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Copyright information

© Universidad Complutense de Madrid 2017

Authors and Affiliations

  1. 1.CMAF-CIO and FCULLisbonPortugal

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