主講人：郭紫華 澳大利亞莫納什大學(xué)教授

時(shí)間：2022年5月13日9：00

地點(diǎn)：騰訊會(huì)議 554 826 155

舉辦單位：數(shù)理學(xué)院

主講人介紹：郭紫華, 2009年博士畢業(yè)于北京大學(xué)，曾任北京大學(xué)講師、副教授。2010.9-2011.8為普林斯頓高等研究院訪(fǎng)問(wèn)學(xué)者，自2015年3月起，任職于澳大利亞Monash大學(xué)副教授。他從事的研究領(lǐng)域?yàn)檎{(diào)和分析以及非線(xiàn)性偏微分方程，在兩個(gè)領(lǐng)域均做出了重要的貢獻(xiàn)。在A(yíng)JM, AIM, JMPA, CMP, AIHP, JFA等國(guó)際著名數(shù)學(xué)雜志發(fā)表重要研究工作四十余篇。 他的工作受到國(guó)內(nèi)外同行的廣泛引用與高度評(píng)價(jià)。

內(nèi)容介紹：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.