Harmonic Analysis Komaba Seminar

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Date, time & place Saturday 13:00 - 18:00 128Room #128 (Graduate School of Math. Sci. Bldg.)

2012/06/09

13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yasuo Furuya (Tokai University) 13:30-15:00
Resent topics on the Cauchy integrals (the works of Muscalu and others) (JAPANESE)
Tsukasa Iwabuchi (Chuo University) 15:30-17:00
Ill-posedness for the nonlinear Schr\\"odinger equations in one
space dimension
(JAPANESE)
[ Abstract ]
In this talk, we consider the Cauchy problems for the nonlinear Schr\\"odinger equations. In particular, we study the ill-posedness by showing that the continuous dependence on initial data does not hold. In the known results, Bejenaru-Tao (2006) considered the problem in the Sobolev spaces $H^s (\\mathbb R)$ and showed the ill-posedness when $s < -1 $. In this talk, we study the ill-posedness in the Besov space for one space dimension and in the Sobolev spaces for two space dimensions.