Young Scholars' Lectures in Analysis and PDE (online seminar)
报告人： Guilong Gui (Northwest University)
Weixi Li (Wuhan University)
时间：2020-06-04 14:00-16:15
地点：ZOOM conference
Speaker: Guilong Gui (Northwest University)
Time： 14:00-15:00 June 4 ，2020
Title: Semiclassical limit of Gross-Pitaevskii equation with Dirichlet boundary condition
Abstract:In this talk, we justify the semiclassical limit of Gross-Pitaevskii equation with Dirichlet boundary condition on the 3-D upper space under the assumption that the leading order terms to both initial amplitude and initial phase function are sufficiently small in some high enough Sobolev norms. We remark that the main difficulty of the proof lies in the fact that the boundary layer appears in the leading order terms of the amplitude functions and the gradient of the phase functions to the WKB expansions of the solutions. In particular, we partially solved the open question proposed in [Chiron and Rousset2009, Pham, Nore and Brachet2005] concerning the semiclassical limit of Gross-Pitaevskii equation with Dirichlet boundary condition. This is a joint work with Prof. Ping Zhang.
Speaker: Weixi Li (Wuhan University)
Time：15:15- 16:15 June 4 ，2020
Title:Well-posedness in Gevrey function space for 3D Prandtl equations without Structural Assumption
Abstract:We establish the well-posedness in Gevrey function space with optimal class of regularity 2 for the three dimensional Prandtl system without any structural assumption. The proof combines in a novel way a new cancellation in the system with some of the old ideas to overcome the difficulty of the loss of derivatives in the system. This shows that the three dimensional instabilities in the system leading to ill-posedness are not worse than the two dimensional ones
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