Structural stability for the Boussinesq equations interfacing with Darcy equations in a bounded domain

Stability of Optimal Controls for the Stationary Boussinesq Equations

The stationary Boussinesq equations describing the heat transfer in the viscous heat-conducting fluid under inhomogeneous Dirichlet boundary conditions for velocity and mixed boundary conditions for temperature are considered. The optimal control problems for these equations with tracking-type functionals are formulated. A local stability of the concrete control problem solutions with respect t...

Dissipative Boussinesq equations

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated nu...

The 2D Incompressible Boussinesq Equations

Global regularity for the viscous Boussinesq equations

∇·u=0 Here is the temperature, u=(u1; u2) is the velocity, p is the pressure. In Reference [1], Pumir and Siggia observed that the cap of a symmetric rising bubble collapses in a nite time. In contrast, E and Shu [2] reported that the motion of the bubble cap is a very unlikely candidate for nite time singularity formation. In this paper, we prove the global regularity for the viscous Boussines...

)-Expansion Method for the Variant Boussinesq Equations

In this paper, by using the improved ( ′ G )-expansion method, we have successfully obtained some travelling wave solutions of the variant Boussinesq Equations. These exact solutions include the hyperbolic function solutions, trigonometric function solutions and rational function solutions. Mathematics Subject Classification: 35Q58; 37K50