For the focusing mass-critical NLS iu, ＋ △u = --｜u｜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, w...For the focusing mass-critical NLS iu, ＋ △u = --｜u｜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 H1 initial data in dimensions d = 2, 3 with spherical symmetry and d ≥ 4 with certain splitting-spherically symmetric initial data.展开更多
基金Acknowledgements The first author is supported in part by National Science Foundation （Grant No. 0908032） and a start up fund in UBC. The second author is supported by an Alfred P. Sloan fellowship.
文摘For the focusing mass-critical NLS iu, ＋ △u = --｜u｜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 H1 initial data in dimensions d = 2, 3 with spherical symmetry and d ≥ 4 with certain splitting-spherically symmetric initial data.
