报告地点：行健楼学术活动室526
邀请人：吴奕飞教授&黄益副教授
摘要：In this talk, I consider the nonlinear Schr\"odinger equation with a general homogeneous nonlinearity in dimension at most three. The power of the nonlinearity is in the mass-subcritical range. We prove the small data scattering in the standard weighted Sobolev space. When the nonlinearity is a gauge-invariant one, the well-posedness and the small data scattering in the framework of the weighted Sobolev space are obtained by using the operator $J(t)=x+it \nabla$. However, when the gauge-invariance is absent, even the local well-posedness is not trivial. Since the usual Duhamel formulation does not work well, we introduce a modified formulation of the equation. In the three-dimensional case, we partially improve the result by Germain, Masmoudi, and Shatah. The talk is based on recent joint work \cite{KMM} with Masaki Kawamoto (Okayama) and Hayato Miyazaki (Kagawa).
