Scattering for the quadratic Klein-Gordon equation

主讲人：郭紫华 澳大利亚莫纳什大学教授

时间：2022年5月13日9：00

地点：腾讯会议 554 826 155

举办单位：数理学院

主讲人介绍：郭紫华, 2009年博士毕业于北京大学，曾任北京大学讲师、副教授。2010.9-2011.8为普林斯顿高等研究院访问学者，自2015年3月起，任职于澳大利亚Monash大学副教授。他从事的研究领域为调和分析以及非线性偏微分方程，在两个领域均做出了重要的贡献。在AJM, AIM, JMPA, CMP, AIHP, JFA等国际著名数学杂志发表重要研究工作四十余篇。 他的工作受到国内外同行的广泛引用与高度评价。

内容介绍：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.