On the convergence of statistical solutions of the 3D Navier-Stokes-α model as α vanishes
نویسنده
چکیده
In this paper statistical solutions of the 3D Navier-Stokes-α model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-α model converge to statistical solutions of the exact 3D Navier-Stokes equations as α goes to zero. The statistical solutions considered here arise as families of time-projections of measures on suitable trajectory spaces.
منابع مشابه
On convergence of trajectory attractors of 3D
We study the relations between the long-time dynamics of the Navier–Stokes-α model and the exact 3D Navier–Stokes system. We prove that bounded sets of solutions of the Navier–Stokes-α model converge to the trajectory attractor A0 of the 3D Navier–Stokes system as time tends to infinity and α approaches zero. In particular, we show that the trajectory attractor Aα of the Navier–Stokes-α model c...
متن کاملTraveling Wave Solutions of 3D Fractionalized MHD Newtonian Fluid in Porous Medium with Heat Transfer
In the present paper, we get exact solutions of Magnetohydrodynamic (MHD) of the fractionalized three-dimensional flow of Newtonian fluid with porous and heat transfer through the traveling wave parameter. The governing equations are produced dependent on established Navier-stokes equations which can be diminished to ordinary differential equation by wave parameter ξ=ax+by+nz+Utα/Γ(α...
متن کاملRooted Trees for 3d Navier-stokes Equation
We establish a representation of the solution of 3d Navier-Stokes equations in the space Φ(α, α) using sums over rooted trees. We study the convergence properties of this series recovering in a simplified manner some results obtained recently by Sinai and other known results. The series representation make sense also in the critical case where there exists global solutions for small initial data.
متن کاملOn the Rate of Convergence of the Two-dimensional Α-models of Turbulence to the Navier-stokes Equations
Rates of convergence of solutions of various two-dimensional α−regularization models, subject to periodic boundary conditions, toward solutions of the exact Navier-Stokes equations are given in the L-L time-space norm, in terms of the regularization parameter α, when α approaches zero. Furthermore, as a paradigm, error estimates for the Galerkin approximation of the exact two-dimensional Leray-...
متن کاملConvergence Analysis and Computational Testing of the Finite Element Discretization of the Navier-Stokes Alpha Model
This report performs a complete analysis of convergence and rates of convergence of finite element approximations of the Navier-Stokes-α (NS-α) regularization of the NSE, under a zero-divergence constraint on the velocity, to the true solution of the NSE. Convergence of the discrete NS-α approximate velocity to the true Navier-Stokes velocity is proved and rates of convergence derived, under no...
متن کامل