Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
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DOI：
10.1103/physrevd.98.104064
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发表时间：
2018-11-30
影响因子：
5
通讯作者：
Noronha, Jorge
中科院分区：
文献类型：
--
作者：
Bemfica, Fabio S.;Disconzi, Marcelo M.;Noronha, Jorge
描述了一种新的方法，以帮助改善相对论粘性流体动力学的基础及其耦合到广义相对论。专注于中性共形流体构造单独的流体动力学变量，我们推导出最一般的粘性能量动量张量产生的二阶导数的运动方程，这是提供了一种新的类型的相对论Navier-Stokes方程的推广，因果关系。我们展示了如何这个能量动量张量可能来自共形动力学理论。我们严格证明本地存在性，唯一性和因果关系的解决方案，这个理论（在充分的非线性制度）在闵可夫斯基背景下，也当流体是动态耦合到爱因斯坦方程。在闵可夫斯基时空平衡点附近的线性扰动在这个因果理论中是稳定的。数值研究揭示了快速膨胀流体存在一个非平衡流体动力吸引子。进一步的属性也进行了研究，并简要讨论了这种方法可以推广到非共形流体。
A new approach is described to help improve the foundations of relativistic viscous fluid dynamics and its coupling to general relativity. Focusing on neutral conformal fluids constructed solely in terms of hydrodynamic variables, we derive the most general viscous energy-momentum tensor yielding equations of motion of second order in the derivatives, which is shown to provide a novel type of generalization of the relativistic Navier-Stokes equations for which causality holds. We show how this energy-momentum tensor may be derived from conformal kinetic theory. We rigorously prove local existence, uniqueness, and causality of solutions of this theory (in the full nonlinear regime) both in a Minkowski background and also when the fluid is dynamically coupled to Einstein's equations. Linearized disturbances around equilibrium in Minkowski spacetime are stable in this causal theory. A numerical study reveals the presence of an out-of-equilibrium hydrodynamic attractor for a rapidly expanding fluid. Further properties are also studied, and a brief discussion of how this approach can be generalized to nonconformal fluids is presented.