摘要
For the focusing mass-critical NLS iut + △u =-|u| 4/d u,it is conjectured that the only global nonscattering solution with ground state mass must be a solitary wave up to symmetries of the equation.In this paper,we settle the conjecture for Hx1 initial data in dimensions d = 2,3 with spherical symmetry and d 4 with certain splitting-spherically symmetric initial data.
For the focusing mass-critical NLS iut + △u =-|u| 4/d u,it is conjectured that the only global nonscattering solution with ground state mass must be a solitary wave up to symmetries of the equation.In this paper,we settle the conjecture for Hx1 initial data in dimensions d = 2,3 with spherical symmetry and d 4 with certain splitting-spherically symmetric initial data.
基金
supported in part by National Science Foundation (Grant No. 0908032)
a start up fund in UBC
supported by an Alfred P. Sloan fellowship
