Singularity formations in the nonlinear Schrodinger-type equations

报告题目:Singularity formations in the nonlinear Schrodinger-type equations

报 告 人:杨开 博士后(Florida International University, USA)




We present two different approaches that showing the stable blow-up solutions in the L^2-critical NLS equation (the log-log blow-up dynamics up to the dimension 12). One approach is the direct numerical simulation via the "Dynamic rescaling method", and then combined with the asymptotic analysis of the rescaled equation. The other approach is to prove the Spectral property with the numerical assistance. Then, use such Spectral property in the analysis to complete the proof. Then, we would like to show the similar numerical results (from the Dynamic rescaling method) that we obtained for the generalized Hartree equation (the NLS equation with non-local potential).


杨开,现为佛罗里达国际大学博士后,本科毕业于四川大学,博士毕业于乔治•华盛顿大学。其研究方向为偏微分方程的奇性分析与数值模拟,在非线性薛定谔的奇性分析方面做出重要成果。已在《Physica D》,《 Nonlinearity》等国际期刊发表多篇学术论文。