From Additive to Transport Noise in 3D Navier-Stokes Equations
摘要
Let \(T>0\) be fixed. Let \(u = u^\epsilon + v^\epsilon \) be the LES decomposition (in the sense of Chapter 1) of three-dimensional Navier-Stokes equations (in this chapter formulated in velocity form on the torus \(\mathbb {T}^3 = (\mathbb {R}/\mathbb {Z})^3\) ), where \(u^\epsilon \) (resp. \(v^\epsilon \) ) denotes the large-scale (resp. small-scale) component of the velocity and \(\epsilon \in (0,1)\) is a small scaling parameter.