In this study we show that, from arbitrarily dispersed initial data, both the concentration of electromagnetic fields and the focusing of gravitational waves could lead to the formation of trapped surfaces. We establish a scale-critical semi-global existence result from the past null infinity for the Einstein-Maxwell system by assigning the signature for decay rates to geometric quantities and Maxwell components. This result generalizes an approach of the first author on studying Einstein vacuum equations by employing additional elliptic estimates and geometric renormalizations, and it also extends a result of Yu to the scale-critical regime.
In this paper, under spherical symmetry we prove a trapped surface formation criterion for the Einstein-Maxwell-charged scalar field system. We generalize an approach introduced by Christodoulou for studying the Einstein-scalar field. In appendix, with double null foliation we also reprove Christodoulou's result and for Minkowskian incoming characteristic initial data, we improve Christodoulou's bound.
For gravitational collapse, we observe a correspondence between region close to past null infinity and region close to central singularity. In line with this philosophy, we construct a new ansatz, with which we first present a 40-page self-contained proof of trapped surface formation in a far-from-center region. A systematical approach with only signature for decay rates is used. Then by a rescaling argument, we convert this result into a reproof and an extension of a scale-critical theorem proved by An-Luk.
A new continuation criterion for the relativistic Vlasov-Maxwell system
相对论性Vlasov-Maxwell方程组在有限能量初值充分正则条件下整体解的存在性是一个长期存在的问题。Alfressey-Strauss（1986）的主要结果表明，只要$f$的动量支撑保持有界，解$(f, E, B)$就保持$C^1$。后来Bouchut-Golse-Pallard（2003）和Klainerman-Staffilani（2002）给出了替代证明。证明了只要$f$在投影到任意二维平面上的动量支集有界，$(f, E, B)$就保持$C^1$ .
We consider the plasma confined in a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, and look at a certain class of equilibria, assuming axisymmetry in the problem. We prove a sharp criterion of spectral stability under these settings. Moreover, we provide several explicit families of stable/unstable equilibria using this criterion.
Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an annular region of the data, for the formation of a future trapped surface. This corresponds to an extension of Christodoulou's classical criterion by the inclusion of the cosmological term.
A Kinetic Concentration criterion for Large-data Boltzmann Dynamics
Tsinghua University（清华大学）；National Center for Theoretical Sciences, National Taiwan University（台湾大学理论科学中心）；Pohang University of Science and Technology（浦项科技大学）
