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四川师范大学 黄娟副教授: Nonlinear Hartree equation in high energy-mass

(发布于:2016-01-05 )

主讲人:  四川师范大学  黄娟副教授

主  题:Nonlinear Hartree equation in high energy-mass

主持人:  经济数学学院 王磊副教授

时  间: 2016年1月7日(星期四) 下午:4:00-5:00

地  点: 通博楼B412

主  办: 经济数学学院、科研处

 

主讲人介绍:

黄娟,女,四川师范大学数学与软件科学学院副教授。已主持国家自然科学基金项目3项。已在《Nonlinear analysis Series A: Theory, Methods & Applications》、《Journal of Mathematical Analysis and Applications》等国内外专业学术刊物上发表论文数篇。曾应邀访问德国波茨坦大学数学所、法国蒙彼利埃第二大学国家科学研究中心。研究方向:非线性波动方程、数学物理。

 

讲座内容:

This talk is concerned with the Cauchy problem of the nonlinear Hartree equation. By constructing a constrained variational problem, we get a refined Gagliardo-Nirenberg inequality and the best constant for this inequality. We thus derive two conclusions. Firstly, by establishing and analyzing the invariant manifolds, we obtain a new criteria for global existence and blowup of the solutions.

Secondly, we get other sufficient condition for global existence with the discussing of the bootstrap argument. And based on these two conclusions, we also deduce so-called energy-mass control maps, which expose the relations hip between the sufficient condition for global existence and the new criteria for global existence and blowup.

 


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