一类非线性Schrdinger方程的整体解和自相似解

THE GLOBAL SOLUTIONS AND SELF-SIMILAR SOLUTIONS FOR A CLASS OF NONLINEAR SCHRDINGER EQUATIONS

对于α的某一取值范围,应用广义Strichartz不等式和压缩映射原理研究了初值在弱L^P空间中足够小的条件下,非线性Schrdinger方程Cauchy问题整体解和自相似解的存在性.

The global Cauchy problem of nonlinear Schroedinger equations is considered by using generalized Strichartz inequalities and the contraction mapping principle. Under some restrictions on parameter α, if the initial value is sufficiently small in some weak L^p space, then there exists a global solution. Moreover, the global unique existence of self-similar solutions is obtained in weak L^p space for the small initial value with self-similar structure.