论文标题
关于二维不可压缩流中能量的保存
On the conservation of energy in two-dimensional incompressible flows
论文作者
论文摘要
我们证明了二维Euler方程的弱和统计解的能量，分别是强（在适当的拓扑）限制中，分别是基础的Navier-Stokes方程和蒙特卡洛 - 光谱粘度数值近似值。我们以所谓的结构函数的均匀衰减来表征这种能量的保存，从而使我们能够扩展现有的能源保护结果。此外，我们提出了具有多种初始数据的数值实验，以验证我们的理论并观察大量二维不可压缩流的能量。
We prove the conservation of energy for weak and statistical solutions of the two-dimensional Euler equations, generated as strong (in an appropriate topology) limits of the underlying Navier-Stokes equations and a Monte Carlo-Spectral Viscosity numerical approximation, respectively. We characterize this conservation of energy in terms of a uniform decay of the so-called structure function, allowing us to extend existing results on energy conservation. Moreover, we present numerical experiments with a wide variety of initial data to validate our theory and to observe energy conservation in a large class of two-dimensional incompressible flows.
