# zbMATH — the first resource for mathematics

On the convergence of solutions of the Leray-$$\alpha$$ model to the trajectory attractor of the 3D Navier-Stokes system. (English) Zbl 1146.35071
The authors study the connection between the long-time dynamics of the Leray-$$\alpha$$ model and the 3D Navier-Stokes equations as $$\alpha \rightarrow 0+$$. It is shown that time shifts of bounded sets of solutions of the Leray-$$\alpha$$ model (in particular the trajectories attractor) converge to the trajectory attractor of the 3D Navier-Stokes system as time tends to infinity and $$\alpha$$ approaches zero.

##### MSC:
 35Q30 Navier-Stokes equations 37L30 Infinite-dimensional dissipative dynamical systems–attractors and their dimensions, Lyapunov exponents 76F20 Dynamical systems approach to turbulence 76F55 Statistical turbulence modeling 76F65 Direct numerical and large eddy simulation of turbulence
Full Text: