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--- 分析与偏微分方程讨论班(2023春季第6讲)

Global existence for the quadratic Dirac equation in two and three space dimensions

张倩

(北京师范大学)

时间：6月26日（周一）10:30-11:30

地点：#腾讯会议：214-478-451

https://meeting.tencent.com/dm/n9MmqVQosonX

摘要: In this report, we study global existence and pointwise decay estimates for the nonlinear Dirac equation with quadratic nonlinearity. We consider four cases depending on the spatial dimension n, the mass parameter m, and the initial data ψ0: i) (n,m)=(2,0) and ψ0 is compactly supported; ii) (n,m)=(3,0) and ψ0 is compactly supported; iii) (n,m)=(3,0) and ψ0 is not necessarily compactly supported; iv) n=3, m≥0 and ψ0 is compactly supported. In each of the cases i)-iii), we prove a small data global existence result, a sharp pointwise decay estimate and a linear scattering result for the global solution. In the case iv) we prove a uniform (in the mass parameter m) global existence result, a unified pointwise decay estimate, and a linear scattering result.

报告人简介: 张倩博士现为北京师范大学在站博士后，博士毕业于北京大学，曾在美国哥伦比亚大学和澳大利亚国立大学交流和工作，在Monge-Ampère方程的边界正则性理论、非线性奇性椭圆方程粘性解的边界正则性、Dirac方程解的整体存在性和点态衰减估计等领域做出成果，并发表在Calc. Var. Partial Differential Equations、J. Differential Equations、J. Geom. Anal.、Ann. Sc. Norm. Super. Pisa Cl. Sci.等期刊上。

邀请人： 张安

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