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On quadratic derivative Schrödinger equations in one space dimension
Stefanov, Atanas G.
Stefanov, Atanas G.
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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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This is the published version, also available here: http://dx.doi.org/10.1090/S0002-9947-07-04207-9. First published in Trans. Amer. Math. Soc. in 2007, published by the American Mathematical Society.
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2007-02-23
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American Mathematical Society
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Stefanov, Atanas G. "On quadratic derivative Schrödinger equations in one space dimension." Trans. Amer. Math. Soc. 359 (2007), 3589-3607. http://dx.doi.org/10.1090/S0002-9947-07-04207-9.