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
Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces
Chengchun Hao, Ling Hsiao, Baoxiang Wang
J. Math. Anal. Appl.: 2007, 328(1), 58--83.
Abstract:We study the well-posedness of Cauchy problem for the fourth order nonlinear Schr?dinger equations $$i\partial_tu=?\varepsilon \Delta u+\Delta^2u+P( (\partial^\alpha_xu)_{|\alpha|\leqslant 2}, (\partial^\alpha_x\bar{u})_{|\alpha|\leqslant 2}),\quad t\in R,\; x\in \mathbb{R}^n,$$ where $\varepsilon\in {?1,0,1}$, $n\geqslant 2$ denotes the spatial dimension and $P(\cdot)$ is a polynomial excluding constant and linear terms.