几何分析与双曲方程会议日程安排
（2016年11月45日、中科院数学所）
会议地点：数学院南楼N913
时间 
报告人 
4号上午09:0009:30 
N913报到 
4号上午09:3010:30 
杨诗武 
4号上午10:4011:40 
王成波 


4号下午14:0015:00 
黎俊彬 
4号下午15:1016:10 
王金花 
4号下午16:3017:30 
马 跃 


5号上午09:3010:30 
黄守军 
5号上午10:4011:40 
王 芳 

报告题目及内容摘要
报告人：杨诗武（北京国际数学中心）
题目： Solutions to the Einsteinscalarfield system in spherical symmetry with large bounded variation norms
摘要： It is wellknown that small, regular, spherically symmetric characteristic initial data to the Einstein scalarfield system which are decaying at (null) infinity give rise to solutions which are global in the sense that they are future causally geodesically complete. In this talk, I will present a construction of a class of global solutions whose data are not required to decay towards infinity. As a consequence, there exist global solutions with arbitrarily large (and in fact infinite) bounded variation (BV) norms and initial Bondi masses. This construction is also extended so that data are posed at past null infinity and we obtain solutions with large BV norms which are causally geodesically complete both to the past and to the future. Finally, I will discuss applications of our method to construct global solutions for other nonlinear wave equations with infinite critical Sobolev norms. This is jointed work with Jonathan Luk and Oh.
报告人：王成波（浙江大学）
题目: The radial Glassey conjecture with minimal regularity
摘要: In this talk, I will report our recent advances on the radial Glassey conjecture with minimal regularity assumption. More precisely, for semilinear wave equations of type $\Box u =\partial_t u^p$ with $p_c = 1 + 2/(n 1)<p<1+2/(n2)$, we prove the global existence for small data in $H^s$ with $s>s_c=n/2+11/(p1)$. It is known that $p>p_c$ is necessary for the problem to admit global solutions and $s\ge s_c$ is necessary for the problem to be local wellposed in $H^s$.
In the process, we exploit and prove a weighted fractional chain rule. We also show wellposedness for 3D quadratic semilinear wave equations with radial data in the almost scalecritical Sobolev space, which improves the earlier result of Klainerman and Machedon.
This is based on the joint work with Kunio Hidano, JinCheng Jiang, Sanghyuk Lee.
报告人：黎俊彬（中山大学）
题目：Formation of trapped surfaces around a spherical singularity of a scalar field
摘要： We extend the famous formation of trapped surfaces result of Christodoulou in 2008, when a massless scalar field is coupled, to the case that the vertex of the initial incoming null cone, which is assumed to be spherically symmetric, is singular. No symmetries are imposed in the solution. The theorem we prove is also an extension to an earlier result of formation of black hole of Christodoulou in spherically symmetry, which is crucial in proving the weak cosmic censorship of the Einsteinscalar field equations in spherical symmetry.
报告人：王金花（厦门大学）
题目：Morawetz estimate for linear gravity on the Schwarzschild spacetime
摘要：
Concerning the linearized gravity for Schwarzschild, the extreme curvature scalars satisfy the Teukolsky equations. Remarkably, analysis of symmetry operators yields transformations between solutions of ReggeWheeler 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
报告人：马跃（西安交通大学）
题目：Nonlinear stability of Minkowski spacetime in f(R) theory and in general relativity with massive scalar field
摘要：In this talk we will present some recent work about the system of Einstein equation coupled with a massive scalar field and the system of f(R) field equation (partially published in [2]). More precisely, we will focus on the nonlinear global stability of the Minkowski spacetime within these two similar contexts. In a PDE point of view, they are equivalent to the global existence of a special class of quasilinear waveKleinGordon system with small initial data.
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 KleinGordon equations in curved spacetime 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 selfgravitating massive field, the waveKleinGordon model. Communications in Mathematical Physics pp 163. First online: 02 January 2016
报告人：黄守军（安徽师范大学）
题目：On smooth solutions to the relativistic string equations in Schwarzschild spacetime and related problems
摘要：This talk mainly considers the motion of relativistic strings in Schwarzschild spacetime. First, we discuss the basic equations for the motion of a pdimensional extended object in a general enveloping spacetime, and then investigate some interesting properties enjoyed by the equations for the motion of relativistic strings in Schwarzschild spacetime. Particularly, the equations are in fact of totally linearly degenerate system of hyperbolic PDEs of first order in (1+1) dimensions. Based on this, under suitable assumptions we are able to prove a smalldata global existence of smooth solutions to the corresponding Cauchy problem. This is a joint work with Professor DeXing Kong and Dr. ChunLei He. In addition, some topics and progress on the relativistic membrane equations are also provided.
报告人：王芳（上海交通大学）
题目： Limit of sharp Sobolev inequalities
摘要： Consider the sharp Sobolev inequalities on the nsphere. By assuming the dimension constant to be a continuous parameter, then the limit of sharp Sobolev inequalities gives the MoserTrudinger inequality as n—>2. However, this is a fake proof of the MoserTrudinger since the dimension constants can only be integers. In this talk, I will mainly introduce a new point of view to make the limit to be mathematically true, by taking advantage of the fractional GJMS operators and their energy extension to the hyperbolic space.
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