论文标题
对于3D Navier-Stokes方程的固定Martingale解决方案的本地规模法律的足够条件
Sufficient conditions for local scaling laws for stationary martingale solutions to the 3D Navier-Stokes equations
论文作者
论文摘要
本文的主要目的是获得足够的条件，使我们能够严格地得出4/5和4/3的局部版本的流体动力湍流定律，我们的意思是，这些法律的版本在有限域中。这是在由Ornstein-Uhlenbeck过程驱动的Navier-Stokes方程的固定Martingale解决方案的背景下完成的。具体而言，我们表明，在\ l^3中的假设\ Say \ Say {平均}前校准，$ local结构函数以长度比例表示为非线性通量，在消失的粘度限制中，并在适当的比例范围内表示。另外，如果人们假设局部能量平等，则等于根据局部耗散表达结构功能。我们的预交性假设还显示出在消失的粘度极限中产生具有相同类型的强迫的Euler方程的固定群溶液。
The main goal of this paper is to obtain sufficient conditions that allow us to rigorously derive local versions of the 4/5 and 4/3 laws of hydrodynamic turbulence, by which we mean versions of these laws that hold in bounded domains. This is done in the context of stationary martingale solutions of the Navier-Stokes equations driven by an Ornstein-Uhlenbeck process. Specifically, we show that under an assumption of \say{on average} precompactness in $L^3,$ the local structure functions are expressed up to first order in the length scale as nonlinear fluxes, in the vanishing viscosity limit and within an appropriate range of scales. If in addition one assumes local energy equality, this is equivalent to expressing the structure functions in terms of the local dissipation. Our precompactness assumption is also shown to produce stationary martingale solutions of the Euler equations with the same type of forcing in the vanishing viscosity limit.
