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We focus on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the nest t-stabilities on certain triangulate...
对于接触Hamilton-Jacobi方程H（x,Du（x）,u（x））=0，H满足Tonelli条件，讨论弱KAM解的结构以及解的Lyapunov稳定性。此外，在单位圆情形时，去掉H关于u 单调性的假设，把条件放宽到对它在一个时间周期内积分平均值的要求，研究它与解的稳定性之间的关系，不稳定时证明不同周期非平凡周期解的存在性，稳定时给出收敛速度。
本报告讨论Hamilton系统辛算法的KAM稳定性，给出辛算法应用于近可积系统时不变环面的存在性证明和数值逼近结果。具体地，近可积系统用辛算法离散化，假设系统的可积部分满足Ruessmann非退化条件，当时间步长足够小且Hamilton函数足够光滑时，离散系统存在不变环面，它们在相应空间中占据一个大测度Cantor集。进而假设系统的可积部分满足Kolmogorov非退化条件，则在Hausdorff...
We use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics of the solutions to the sine-Gordon equation whose initial condition belongs to some weighted So...
In this talk, we discuss the global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindbla...
We consider the existence, uniqueness and nonlinear stability of the travelling wave solution of the Navier-Stokes-Poisson system with density-dependent viscosity for ions. Firstly, we derive a system...
In this talk, we talk about the proof of the O(2)-symmetry of 3D steady gradient solitons. The proof consists of four parts: the asymptotic analysis at infinity, the symmetry improvement theorem, the ...
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant po...
In his pioneering work in 1860, Riemann proposed the Riemann problem and solved it for isentropic gas in terms of shocks and rarefaction waves. It eventually became the foundation of the theory of one...
O-minimal structures have been introduced in the 80s to some extent with the goal of finding generalizations of model theoretic properties of stable theories to ordered structures. Later on, numerous ...
In this talk, the combined quasi-neutral and zero-viscosity limits of the two-fluid Navier-Stokes-Poisson systems (one for ion and another for electron) with boundary are rigorously proved by investig...
本报告中，我们讨论接触型定态Hamilton-Jacobi解的稳定性，演化方程解的长期行为，和非平凡周期解的存在性。
We expect that the study of pluricanonical systems of varieties of general type with many global forms can be reduced to the study of pluricanonical systems of varieties of lower dimensions. We show t...
本报告我们主要介绍相对论性带电流体的拉氏量表述及相关稳定性分析的一些新进展。

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