On quadratic derivative Schrödinger equations in one space dimension

• Autores: Atanas Stefanov
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 8, 2007, págs. 3589-3607
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04207-9
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• Resumen

  • 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.