Self-similarity in viscous 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...

Global Well-posedness of the Viscous Boussinesq Equations

We prove the global well-posedness of the viscous incompressible Boussinesq equations in two spatial dimensions for general initial data in Hm with m ≥ 3. It is known that when both the velocity and the density equations have finite positive viscosity, the Boussinesq system does not develop finite time singularities. We consider here the challenging case when viscosity enters only in the veloci...

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

Similarity solution of the Boussinesq equation

Similarity transforms of the Boussinesq equation in a semi-in®nite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial di€erential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15±36] use a hodograph method to derive an integral equation formulation of the new di€erential equation which they sol...