EXISTENCE OF SOLUTIONS OF THE $g$-NAVIER-STOKES EQUATIONS

Abstract

The g-Navier-Stokes equations in spatial dimension 2 are the following equations introuduced inwith the continuity equation 1 g r ¢ (gu) = 0:Here, we show the existence and uniqueness of solutions of g-Navier-Stokes equations on R n for n = 2;3.

Large-domain stability of random attractors for stochastic g-Navier–Stokes equations with additive noise

“…Proof By taking σ = τ in (45), we find that Φ k has an absorbing set M k given by We need to prove that ρ 1 and ρ 2 are tempered with the growth rate 3 On the other hand, by Corollary 2, Φ k is D k -pullback asymptotically compact. Therefore, it follows from the abstract result [21] that Φ k has a unique D k -pullback random attractor denoted by A k = {A k (τ , ω)}.…”

On the weak solutions and determining modes of the g-Benard Problem

“…Then we have v1 = u1, v2 = u2 and from the incompressibility condition (1.2) we have ∇ • (gv) = 0. Therefore, (see, [35,1]…”

“…Following the technique given in [39,3], as m → ∞ we obtain ) for Ψ1(t), Ψ2(t) ∈ C ∞ 0 (0, T ) we see that {u, θ} satisfy (3.1) and (3.2). Furthermore, applying similar techniques given in [39,1] it is easy to show that {u, θ} satisfy the initial conditions u(0) = u0 and θ(0) = θ0.…”

Spectral Galerkin Method in Space and Time for the 2Dg-Navier-Stokes Equations

“…In the last few years, the existence and long-time behavior of both weak and strong solutions to the 2D -Navier-Stokes equations have been studied extensively (cf. [2][3][4][5][6][7][8][9]). In this paper, we aim to study numerical approximation of the strong solutions to problem (1).…”