Global solvability of some double-diffusive convection system coupled with Brinkman-Forchheimer equations

Abstract

In this paper, the global solvability of the initial boundary value problem and the periodic problem are discussed for a doublediffusive convection system under the homogeneous Neumann boundary condition in a bounded domain. This system is coupled with the so-called Brinkman-Forchheimer equations, which is similar to the Stokes equations and contains some convection terms similar to that in the Navier-Stokes equations. However, in contrast to the Navier-Stokes equations, it is shown that the global solvability in L 2 -spaces holds true for the 3-dimensional problems.

Attractors for autonomous double‐diffusive convection systems based on Brinkman–Forchheimer equations

“…For Neumann boundary condition case, we can derive almost the same result as that for Dirichlet boundary condition case from [14].…”

“…Let be a suitable constant satisfying the following inequality (see [14], Sohr [24] and Temam [25]):…”

“…2 than those in [11] and [12]. In this paper, we consider the existence of global attractor and exponential attractor of (DCBF) in…”

“…1 H 1 , we need to establish more minute a priori estimates than those in [14]. To cope with this difficulty, we rely on an abstract result given in Brézis [15] (see Lemma 3.1 given in Section 3).…”

Solvability of <i>p</i>-Laplacian Parabolic Equations with Constraints Coupled with Navier-Stokes Equations in 3D Domains by Using Largeness of <i>p</i>

“…r Remark 3.1. The solvability of nonlinear evolution equations of NavierStokes type, in a strong sense such that Dv and dv=dt make sense in L 2 , is derived by methods for subdi¤erential operators with nonmonotone perturbations in an abstract framework in Ô tani [17], and there are several applications of [17] (see e.g., Ô tani-Uchida [18]). This abstract theory is an elegant result using D. Brézis's interpolation ( [2]).…”