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甬江数学讲坛84-86讲(2020年第11-13讲)

发布日期:2020-07-07 作者:数学与统计学院 文章来源:未知  责任编辑:

报告时间:202078日上午9点开始

报告地点:腾讯会议在线报告

会议链接:http://meeting.tencent.com/s/1LW7Ycuv7w23

会议 ID532 121 084

 

 

报告题目1Scattering for quadratic Klein-Gordon equation

:郭紫华(澳大利亚莫纳什大学 教授)

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.  

报告人简要:郭紫华教授现在澳大利亚莫纳什大学任教,主要研究调和分析及其在非线性发展方程中的应用,在色散方程的低正则性,长时间渐进行为,稳定性等重要课题上做出了一系列具有国际影响力的工作,主要结果发表在AJMADV MATHCMP, JMPA, C R Acad Sci Paris Ser I Math等国际重要期刊


报告题目2Long time asymptotics for the sine-Gordon equation

:刘家琪(Toronto大学  副教授)

报告摘要:We calculate the long time asymptotic formula for the sine-Gordon equation on the real line. Radiation term and kink/breather stability will be discussed. Our approach is based on the nonlinear steepest descent method for oscillatory Riemann-Hilbert problems. This is joint work with Gong Chen and Bingying Lu.

报告人简要:刘家琪现在Toronto大学从事研究工作,主要研究数学物理中的可积系统,反散射理论,谱理论等,在孤立子分解,算子谱理论等重要课题上做出了一系列工作,主要结果发表在CMPCPDE等国际重要期刊。


报告题目3 Long-time asymptotics for the cubic NLS in 1d

人:陈功Fields institute/肯塔基大学 副教授)

报告摘要:I will discuss the long-time asymptotics of small solutions to the 1d cubic NLS with a potential. Using distorted Fourier transforms, localized dispersive estimates, we obtain the long-time asymptotics for the 1d cubic NLS under very mill assumptions on potentials. This is joint work with Fabio Pusateri.

报告人简要:陈功在芝加哥大学取得博士学位,在Toronto大学从事博士后研究, 现在Fields institute任教。主要研究色散方程和可积系统,在孤立子稳定性,多孤立子构造,可积系统的低正则性,可积系统的渐进行为等重要课题上做出了一系列工作,主要结果发表在Memoirs AMSCMP等国际重要期刊

 


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