Local Well-Posedness for the Derivative Nonlinear Schrödinger Equation in Besov spaces

2016/11/17 by Cai Constantin Cloos, Cloos, Cai Constantin
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1611.05628

25 pages

arxiv created 2016/11/17 · arxiv updated 2016/11/18

Abstract

It is shown that the cubic derivative nonlinear Schrödinger equation is locally well-posed in Besov spaces B^s_2,∞(\mathbb X), s≥\tfrac12, where we treat the non-periodic setting \mathbb X=\mathbb R and the periodic setting \mathbb X=\mathbb T simultaneously. The proof is based on the strategy of Herr for initial data in H^s(\mathbb T), s≥\tfrac12.

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