On the basis of the integrable Kaup-Boussinesq version of the shallow water equations, an analytical theory of undular bores is constructed. The problem of the decay of an initial discontinuity is considered.

In this paper we study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.

In this article, we consider the two-dimensional dissipative Boussinesq systems which model surface waves in three space dimensions. The long time asymptotics of the solutions for a large class of such systems are obtained rigorously for small initial data.

We prove the nonlinear stability and convergence of a fully discrete, pseudospectral scheme for the "good" Boussinesq equation un = -uxxxx + uxx + ("2)xx ■ Numerical comparisons with finite difference schemes are also reported.

We consider the full Navier-Stokes-Fourier system in the singular limit for the small Mach and large Reynolds and Péclet numbers, with ill prepared initial data on R 3. The Euler-Boussinesq approximation is identified as the limit system.

We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer.

In this report, generalized wave breaking equations are developed using three dimensional fully nonlinear extended Boussinesq equations to encompass rotational dynamics in wave breaking zone. The derivation for vorticity distributions are developed from Reynold based stress equations.

We establish the existence of a stationary weak solution of a generalized Boussinesq model for thermally driven convection in exterior domains. We use the fact that the exterior domain can be approximated by interior domains.

In this paper, we propose the extended Boussinesq–Whitham–Broer–Kaup (BWBK)-type equations with variable coefficients and fractional order. We consider BWBK equations, Whitham–Broer–Kaup (WBK) Boussinesq by setting proper smooth functions that are derived from proposed equation. obtain uniformly coupled traveling wave solutions of considered employing improved system method, subsequently their ...