Wellposedness of Cauchy problem for the Fourth Order Nonlinear Schrödinger Equations in Multi-dimensional Spaces

Hao, Chengchun; Hsiao, Ling; Wang, Baoxiang

Wellposedness of Cauchy problem for the Fourth Order Nonlinear Schrödinger Equations in Multi-dimensional Spaces

Authors

Hao, Chengchun

Hsiao, Ling

Wang, Baoxiang

Description

We study the wellposedness of Cauchy problem for the fourth order nonlinear Schrödinger equations i\partial_t u=-\epsΔu+Δ^2 u+P((\partial_x^αu)_{\absα\ls 2}, (\partial_x^α\bar{u})_{\absα\ls 2}),\quad t\in \Real, x\in\Real^n, where $\eps\in\{-1,0,1\}$, $n\gs 2$ denotes the spatial dimension and $P(\cdot)$ is a polynomial excluding constant and linear terms.
28 pages