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研究员、博士生导师,中国科学院数学与系统科学研究院 数学研究所 | Professor, Institute of Mathematics, AMSS, CAS
Well-posedness for one-dimensional derivative nonlinear Schrödinger equations
Chengchun Hao
Commun. Pure Appl. Anal.: 2007, 6(4), 997--1021.
Abstract:In this paper, we investigate the one-dimensional derivative nonlinear Schr\"odinger equations of the form $iu_t-u_{x x}+i\lambda |u|^k u_x=0$ with non-zero $\lambda\in \mathbb R$ and any real number $k\geq 5$. We establish the local well-posedness of the Cauchy problem with any initial data in $H^{1/2}$ by using the gauge transformation and the Littlewood-Paley decomposition.