弱于H^1空间的L^2-临界非线性Schrdinger方程的柯西问题

Cauchy Problem for the L^2-Critical Nonlinear Schrdinger Equation Below H^1

讨论H^s(R^n)(n≥1,1-ε<s<1)中L^2-临界焦聚型非线性Schrdinger方程的柯西问题,这里ε>0是一个可以表出的很小的数.主要结论给出了在有限时间破裂解的L^2集中现象.同时,作为推论,得到了小初值解的整体存在性.

This paper studies solutions of the L^2-critical focusing nonlinear Schroedinger equation in H^s（R^n） （n ≥ 1, 1-ε 〈 s 〈 1）, for some small ε 〉 0, the expression can be given. This main result gives the L2 concentration phenomena for finite time blow up solution, and as a corolary, the global well-posedness for small initial data is obtained.