Demetrios Christodoulou 系列学术报告[Apirl 15-22, 2009](new)
2009-04-14 来源：数学科学研究中心活动地点：
活动类型：学术报告
主讲人：Demetrios Christodoulou
活动时间：
活动内容：
Speaker: Professor Demetrios Christodoulou (ETH Zürich)
1、时间：2009-4-15(周三) 4:00-5:00pm
地点：CMS 202
题目：The formation of black holes in general relativity: Part 1
2、时间：2009-4-17(周五) 4:00-5:00pm
地点：CMS 203
题目：The formation of black holes in general relativity: Part 2
Abstract: In 1965 Penrose introduced the fundamental concept of a trapped surface, on the basis of which he proved a theorem which asserts that a spacetime containing such a surface must come to an end. The presence of a trapped surface implies, moreover, that there is a region of spacetime, the black hole, which is inaccessible to observation from infinity.
A major challenge since that time has been to find out how trapped surfaces actually form, by analyzing the dynamics of gravitational collapse. I recently published a monograph which achieves this aim by establishing the formation of trapped surfaces in pure general relativity through the focusing of gravitational waves.
The theorems proved in the monograph constitute the first foray into the long-time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitable neighborhood of trivial data. The main new method, the short pulse method, applies to general systems of Euler-Lagrange equations of hyperbolic type, and provides the means to tackle problems which have hitherto seemed unapproachable.
3、时间：2009-4-20(周一) 4:00-5:00pm
地点：CMS 201
题目：The formation of shocks in 3-dimensional fluids: Part 1
4、时间：2009-4-22(周三) 4:00-5:00pm
地点：CMS 202
题目：The formation of shocks in 3-dimensional fluids: Part 2
Abstract: The equations describing the motion of a perfect fluid were first formulated by Euler in 1752. These equations were among the first partial differential equations to be written down, but, after the lapse of two and a half centuries, we are still far from adequately understanding the observed phenomena which are supposed to lie within their domain of validity.
These phenomena include the formation and evolution of shocks in compressible fluids. The first work on shock formation was done by Riemann in 1858. However, his analysis was limited to the simplified case of one space dimension. Since then, several deep physical insights have been attained and new methods of mathematical analysis invented. Nevertheless, the theory of the formation and evolution of shocks in real three-dimensional fluids has remained fundamentally incomplete.
In 2007 I published a monograph which considers the relativistic Euler equations in three space dimensions for a perfect fluid with an arbitrary equation of state. I considered initial data for these equations which outside a sphere coincide with the data corresponding to a constant state. Under a suitable restriction on the size of the initial departure from the constant state, I established theorems that give a complete description of the maximal classical development. In particular, I showed that the boundary of the domain of the maximal classical development has a singular part where the inverse density of the wave fronts vanishes, signalling shock formation. The theorems give a detailed description of the geometry of this singular boundary and a detailed analysis of the behavior of the solution there. A complete picture of shock formation in three-dimensional fluids is thereby obtained. The approach is geometric, the central concept being that of the acoustical spacetime manifold.
