一类四阶非线性Schro^¨dinger方程的爆破准则

Blow-Up Criteria for a Kind of Fourth Order Nonlinear Schro^¨dinger Equations

摘要: 本文通过改进的B-G型不等式研究了一类四阶非线性Schro^¨dinger方程的初边值问题。首先借助半群理论得到初值问题局部解的存在唯一性，其次利用B-G型不等式得到了初值问题经典解整体存在的一个新判定准则，即整体解是否存在可由其H²范数是否爆破决定。

Abstract: The initial-boundary value problem for a kind of fourth order nonlinear Schro^¨dinger equations is studied in this paper. Firstly, with the help of the semi-group theory, the existence and uniqueness of local solution of initial value problem is obtained. Secondly, a new global existence criterion for the classical solution is given by using B-G inequality, namely, that whether the solution globally exists is determined by whether its H² norm blows up.