报告题目：Cosmological Newtonian limits on large scales
报告时间：2018年6月26日，上午10:30-11：30
地点：18-925
报告人：刘超（北大国际数学中心）
摘要： I will give a very brief overview of the rigid mathematical proof of one basic question in cosmological simulation: on what space and time scales Newtonian cosmological simulations can be trusted to approximate relativistic cosmologies?
We resolve this question by investigating Einstein-Euler systems with positive cosmological constant and Poisson-Euler systems under a small initial data condition. Informally, we establish the initial data set in the meaning of cosmological scale which solves constraint equations and construct the existence of 1-parameter families of $\epsilon$-dependent solutions to Einstein-Euler systems with a positive cosmological constant that:
(1) are defined for $\epsilon \in (0,\epsilon_0)$ for some fixed constant $\epsilon_0>0$,
(2) exist globally on $(t,x^i)\in[0,+\infty)\times \mathbb{R}^3$, % and are geodesically complete to the future,
(3) converge, in a suitable sense, as $\epsilon \searrow 0$ to solutions of the cosmological Poison-Euler equations of Newtonian gravity, and
(4) are small, non-linear perturbations of the FLRW fluid solutions (via conformal singular formulation of Einstein-Euler system).
This talk originates from a joint work with Todd Oliynyk.
报告人简介：刘超， 男， 北京大学北京国际数学中心博士后，澳大利亚Monash大学博士毕业。主要研究兴趣是偏微分方程，数学广义相对论，严格牛顿极限理论和相对论流体。
