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Seminar
FIELD Math:Analysis
DATE August 11 (Tue), 2020
TIME 16:00-18:00
PLACE 1423
SPEAKER 이기연
HOST Lee, Jinyeop
INSTITUTE Jeonbuk National University
TITLE [GS_M_APP] On the global well-posedness of focusing energy-critical inhomogeneous NLS: weighted space approach
ABSTRACT We give a survey of the focusing energy-critical inhomogeneous nonlinear Schr\"odinger equation(NLS). The cubic NLS can be a physical model of dilute Bose-Einstein condensate when the two-body interation of the condensate are considered. The global well-posedness(GWP) of energy-critical homogeneous NLS is well-known for the results of Kenig and merle in 2006. In this talk we will show the GWP, scattering results for radial solutions to energy-critical inhomogeneous NLS and blowup results for the radial solutions solutions under some energy conditions related to stationary problem of homogeneous NLS. We also show the nonexistence of positive radial solution to critical stationary problem of the inhomogeneous NLS. nhomogeneous coefficient index $b$ can be extended to $\frac32$ via weighted space. This talk is based on co-work with Yonggeun Cho and Seokchang Hong.
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