2016114-5日、中科院数学所）

 时间 报告人 4号上午09:00----09:30 N913报到 4号上午09:30----10:30 杨诗武 4号上午10:40----11:40 王成波 4号下午14:00----15:00 黎俊彬 4号下午15:10----16:10 王金花 4号下午16:30----17:30 马  跃 5号上午09:30----10:30 黄守军 5号上午10:40----11:40 王  芳

In the process, we exploit and prove a weighted fractional chain rule. We also show well-posedness for 3-D quadratic semi-linear wave equations with radial data in the almost scale-critical Sobolev space, which improves the earlier result of Klainerman and Machedon.

This is based on the joint work with Kunio Hidano, Jin-Cheng Jiang, Sanghyuk Lee.

Concerning the linearized gravity for Schwarzschild, the extreme curvature scalars satisfy the Teukolsky equations. Remarkably, analysis of symmetry operators yields transformations between solutions of Regge-Wheeler and Teukolsky. We prove the pointwise decay for the Regge Wheeler equation, and this gives strong pointwise decay for Teukolsky. This is joint work with Steffen Aksteiner and Lars Andersson

To the author's knowledge there is not so much choice to deal with this kind of system (for a detailed explication of the major difficulty, see for example in [1] page 2), and we apply the hyperboloidal foliation method introduced by the author in [1] combined with some newly developed tools such as L1 estimates on Klein-Gordon equations in curved space-time and L1 estimates on wave equations based on the expression of spherical means. We also adapt some tools developed in classical framework for the analysis of Einstein equation into our hyperboloidal foliation framework, such as the estimates based on wave gauge conditions and the L1 estimates on wave equations based on integration along characteristics.

Reference:

[1] P. LeFloch and Y. Ma, The hyperboloidal foliation method, World Scientific, 2015

[2] P. LeFloch and Y. Ma, The nonlinear stability of Minkowski space for self-gravitating massive field, the wave-Klein-Gordon model.  Communications in Mathematical Physics pp 1-63. First online: 02 January 2016