Global well-posedness of the two-dimensional horizontally filtered simplified Bardina turbulence model on a strip-like region

Abstract

We consider the 2D simplified Bardina turbulence model, with horizontal filtering, in an unbounded strip-like domain. We prove global existence and uniqueness of weak solutions in a suitable class of anisotropic weighted Sobolev spaces.

Exponential Attractors for the 3D Fractional-order Bardina Turbulence Model With Memory and Horizontal Filtering

“….g., [5,6,12,14]) coupled with the stronger dissipation term −ν w, i.e. a full Laplacian appears instead of ν 2β w in (6) (and also in (9)).…”

Remark on a Regularity Criterion in Terms of Pressure for the 3D Inviscid Boussinesq–Voigt Equations

“…Hence, we reach where we employed Hölder's and Young's inequalities. Now, we can use this last inequality to make explicit the terms, involving the spacederivatives of , needed to reach (6). To do so, we follow the same line of reasoning as in the proof of [28,Theorem 2.2].…”

“…There is a wide range of -approximation models for the Navier-Stokes equations and for other related systems in fluid dynamics (see, for instance, [1,9,12,17,23], see also [6]). Further details can be found in [8,9].…”

On the existence of an inertial manifold for a deconvolution model of the 2D mean Boussinesq equations

“…Here, we consider the approximate deconvolution model, introduced by Adams and Stolz (see also previous studies); by following this scheme, we approximate the filtered bilinear terms as follows: where v and φ play the role of the variables u and θ , respectively, and the filtering operator G α is defined by the Helmholtz filter (see, eg, other studies; see also Bisconti and Catania for an analogous case involving an anisotropic horizontal filter), with and G α :=( I − α 2 Δ) −1 . Here, D N is the deconvolution operator, which is constructed using the Van Cittert algorithm (see, eg, Lewandowski) and is formally defined by …”

“…where v and play the role of the variables u and , respectively, and the filtering operator G is defined by the Helmholtz filter (see, eg, other studies [9][10][11][12] ; see also Bisconti and Catania 13,14 for an analogous case involving an anisotropic horizontal filter), with (·) = G (·) and G ∶= (I − 2 Δ) −1 . Here, D N is the deconvolution operator, which is constructed using the Van Cittert algorithm (see, eg, Lewandowski 10 ) and is formally defined by…”