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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
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