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  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).