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Decay estimates for Schrödinger equations

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Abstract

We prove global existence and optimal decay estimates for classical solutions with small initial data for nonlinear nonlocal Schrödinger equations. The Laplacian in the Schrödinger equation can be replaced by an operator corresponding to a non-degenerate quadratic form of arbitrary signature. In particular, the Davey-Stewartson system is included in the the class of equations we discuss.

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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, 5734 University Avenue, 60637, Chicago, IL, USA

    Peter Constantin

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  1. Peter Constantin
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Communicated by B. Simon

Partially supported by NSF grant DMS-860-2031. Sloan Research Fellow

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Constantin, P. Decay estimates for Schrödinger equations. Commun.Math. Phys. 127, 101–108 (1990). https://doi.org/10.1007/BF02096495

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  • DOI: https://doi.org/10.1007/BF02096495

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