论文标题
Kasner奇点附近的相对论完美流体
Relativistic perfect fluids near Kasner singularities
论文作者
论文摘要
我们建立了在奇异性附近的Kasner背景上稳定的解决方案的稳定解决方案家族，具有完整的预期渐近数据自由度，而无对称或各向同性限制。存在是通过将Euler方程转换为对称双曲线紫红色系统的形式来实现的，然后将新存在理论应用于单一初始值问题的应用。稳定性显示出源自Arxiv：1907.04071（1907.04071）的（常规）全局初始值问题的存在理论。实际上，对于家庭中的每种解决方案，我们证明了具有相同定性渐近剂的一组开放式解决方案的存在，并表明任何这种扰动的溶液再次与单个初始值问题的另一种解决方案一致。我们所有的结果都在与所有Kasner指数相比，流体声音速度很大的制度。这被解释为Kasner Big Bang Singularies附近的稳定流体渐近技术的政权。
We establish the existence of a stable family of solutions to the Euler equations on Kasner backgrounds near the singularity with the full expected asymptotic data degrees of freedom and no symmetry or isotropy restrictions. Existence is achieved through transforming the Euler equations into the form of a symmetric hyperbolic Fuchsian system followed by an application of a new existence theory for the singular initial value problem. Stability is shown to follow from the existence theory for the (regular) global initial value problem for Fuchsian systems that was developed in arXiv:1907.04071. In fact, for each solution in the family, we prove the existence of an open set of nearby solutions with the same qualitative asymptotics and show that any such perturbed solution agrees again with another solution of the singular initial value problem. All our results hold in the regime where the speed of sound of the fluid is large in comparison to all Kasner exponents. This is interpreted as the regime of stable fluid asymptotics near Kasner big bang singularities.
