郝成春的个人主页 | Chengchun HAO's Homepage
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
Wellposedness for the fourth order nonlinear Schrödinger equations
Chengchun Hao, Ling Hsiao, Baoxiang Wang
J. Math. Anal. Appl.: 2006, 320(1), 246--265.
Abstract:We study the local smoothing effects and wellposedness of Cauchy problem for the fourth order nonlinear Schr?dinger equations in 1D $$i\partial_tu=\partial_x^4 u+P((\partial^\alpha_xu)_{|\alpha|\leqslant 2}, (\partial^\alpha_x\bar{u})_{|\alpha|\leqslant 2}),\quad t,x\in R,$$ where $P(\cdot)$ is a polynomial excluding constant or linear terms.