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