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Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations. (English) Zbl 1479.35101

Exner, Pavel (ed.) et al., Partial differential equations, spectral theory, and mathematical physics. The Ari Laptev anniversary volume. Berlin: European Mathematical Society (EMS). EMS Ser. Congr. Rep., 209-229 (2021).
Summary: We prove existence of the global attractor of the damped and driven 2D Euler-Bardina equations on the torus and give an explicit two-sided estimate of its dimension that is sharp as \(\alpha\to 0^+\).
For the entire collection see [Zbl 1465.35005].

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
35B45 A priori estimates in context of PDEs
35Q31 Euler equations
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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