On quadratic derivative Schrödinger equations in one space dimension

Stefanov, Atanas

doi:10.1090/S0002-9947-07-04207-9

On quadratic derivative Schrödinger equations in one space dimension
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Trans. Amer. Math. Soc. 359 (2007), 3589-3607 Request permission

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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