On the convergence of the uniform attractor for the 2D Leray-\(\alpha\) model. (English) Zbl 1433.35264

Deugoué, Gabriel

Abstr. Appl. Anal. 2017, Article ID 1681857, 11 p. (2017).

Summary: We consider a nonautonomous 2D Leray-\(\alpha\) model of fluid turbulence. We prove the existence of the uniform attractor \(\mathcal{A}^\alpha\). We also study the convergence of \(\mathcal{A}^\alpha\) as \(\alpha\) goes to zero. More precisely, we prove that the uniform attractor \(\mathcal{A}^\alpha\) converges to the uniform attractor of the 2D Navier-Stokes system as \(\alpha\) tends to zero.

MSC:

35Q35	PDEs in connection with fluid mechanics
35B41	Attractors
37L30	Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
76F20	Dynamical systems approach to turbulence

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