On illposedness for the cubic NLS equation on the circle
主 题: On illposedness for the cubic NLS equation on the circle
报告人: Professor Luc Molinet (University Francois rabelais, Tours)
时 间: 2010-06-18 14:30 - 16:00
地 点: 理科一号楼 1479
We prove the ill-posedness in Hs(T), s < 0, of the periodic cubic Schrodinger equation in the sense that the flow-map is not continuous from Hs(T) into itself for any fixed t\ne 0. This result is slightly stronger than the one in [7] where the discontinuity of the solution map is established. Moreover our proof is different and clarifies the ill-posedness phenomena. Our approach relies on a new result on the behavior of the associated flow-map with respect to the weak topology of L2(T).
