不可压非相对论性纳维-斯托克斯方程的引力解
The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
摘要：
我们注意到，相对论流体力学方程在特定的尺度极限下可化为不可压的纳维-斯托克斯方程。在这个极限中，底层相对论系统的边界度规涨落变成了一个与背景电磁场对有效带电流体的作用相同的强迫函数。我们证明了特殊的共形对称的父相对论理论下降到“加速助推”对称的纳维-斯托克斯方程，揭示了一个可能的新的共形对称结构，这些方程。应用我们的缩放限制全息诱导流体动力学，我们发现重力的双重描述的任意解的强迫非相对论不可压缩纳维-斯托克斯方程。在全息的情况下，我们还发现了一个简单的强迫稳态剪切解的纳维-斯托克斯方程，并证明，这种解决方案在足够高的雷诺数不稳定，表明可能最终过渡到湍流。
英文摘要：
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to `accelerated boost' symmetries of the Navier-Stokes equations, uncovering a possibly new conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.
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