Initial Boundary Value Problem for Two-Dimensional Viscous Boussinesq Equations

Global regularity results for the 2D Boussinesq equations with vertical dissipation

“…Danchin and Paicu very recently explored the global regularity issue for the cases when there is either horizontal dissipation (ν 1 > 0 and ν 2 = κ 1 = κ 2 = 0) or horizontal thermal diffusion (κ 1 > 0 and ν 1 = ν 2 = κ 2 = 0) and obtained global solutions at several regularity levels (see [11]). Other interesting recent results on the 2D Boussinesq equations can be found in [1,9,10,12,13,17,20,22]. The global regularity problem for the Boussinesq equations with vertical dissipation and thermal diffusion, namely (1.1), was first studied by Adhikari et al in [2].…”

Global regularity for a coupled Cahn-Hilliard-Boussinesq system on bounded domains

“…[27,30]) and has been well studied in the literature. The readers are referred to [9,11,12,18,19] and the references therein for the Cauchy problem, and to [22,26,32] and the references therein…”

Strong solutions and inviscid limit for Boussinesq system with partial viscosity

“…Indeed, as far as we know, only a few works are devoted to the study of the Boussinesq system with partial viscosity (κ = 0) in bounded or exterior domains. For instance, we have found in the literature the work [22] where the authors studied the existence of classical solutions for (1.2)-(1.3) with v > 0 being a constant, Ω a bounded domain, and H 3 -initial data (see also [8] for v = 0).…”