On the convergence of statistical solutions of the 3D Navier-Stokes-$\alpha$ model as $\alpha$ vanishes

Abstract

In this paper statistical solutions of the 3D Navier-Stokes-$\alpha$ model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-$\alpha$ model converge to statistical solutions of the exact 3D Navier-Stokes equations as $\alpha$ goes to zero. The statistical solutions considered here arise as families of time-projections of measures in suitable trajectory spaces.

References in corpus (2)

• Analysis of a General Family of Regularized Navier-Stokes and MHD Models
• Inviscid limit for damped and driven incompressible Navier-Stokes equations in ${\mathbb{R}}^2$

Cited by in corpus (1)

• Trajectory Statistical Solutions for three-dimensional Navier-Stokes-like systems