报告题目：Scattering for quadratic Klein-Gordon equation
报告人：郭紫华（澳大利亚莫纳什大学副教授）
报告时间：2020年6月30日14时00分
腾讯会议号：853 651 696，密码：0630
邀请人：程 星
报告摘要：
In this talk, I will talk about the scattering problem for the Klein-Gordon equation with quadratic nonlinear term in dimensions 3 and 4. In the first part, I will review the scattering theory using nonlinear Schrodinger equations as examples. The scattering problem in energy space for low order nonlinearity and low dimensions is more difficult even for small data. Quadratic Klein-Gordon equation is mass-subcritical in 3D and mass-critical in 4D. Only small data scattering results were known before. In the second part, I will talk about the recent joint works with Jia Shen. For 3D radial case, we give an alternative proof for small energy scattering and partial results for large data. For 4D we prove large data scattering below the ground state. In 4D radial case, the proof is done by combining radial improved Strichartz estimates, normal form technique and Dodson-Murphy's idea, while the non-radial case is done by concentration-compactness method.
报告人简介：
郭紫华，澳大利亚莫纳什大学数学学院副教授。主要从事调和分析与偏微分方程的研究，具体地，郭紫华副教授在非线性色散方程、振荡积分与色散估计、微分算子相关的调和分析问题、流体力学方程等方向开展研究。曾主持国家自然科学基金面上基金、国家自然科学基金青年基金、澳大利亚ARC基金。此外，郭紫华在国内工作期间入选多项国家创新人才项目。
郭紫华副教授共发表41篇学术论文， 特别地，在Math. Ann., Adv. Math., J. Math. Pures Appl., Anal. PDE, Comm. Math. Phys., J. Funct. Anal., SIAM J. Math. Anal., Comm. Partial Differential Equations等国际著名数学杂志发表重要研究工作，他的工作受到国内外同行的广泛关注。