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.

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

A family of Boussinesq systems has recently been proposed by Bona, Chen, and Saut in [J.L. Bona, M. Chen, J.-C. Saut, Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I. Derivation and linear theory, J. Nonlinear Sci. 12 (4) (2002) 283–318] to describe the two-way propagation of small-amplitude gravity waves on the surface of water in a canal....

For flows with small density variations, it is convenient to approximate them as incompressible whilst retaining the leading order effects due to the density variations, thus avoiding issues associated with acoustic waves. The classical approach is the Boussinesq approximation which was originally motivated by the desire to account for gravitational buoyancy effects. There are many situations o...

This article is a review of [6], which is concerned with the scattering theory for the Schrödinger-improved Boussinesq system in two space dimensions.

A solution is presented to a doubly mixed boundary value problem of the torsion of an elastic layer, partially resting on a rigid circular base by a circular rigid punch attached to its surface. This problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer expansion formula of the Bessel f...

We propose a modi…cation of the classical Navier-Stokes-Boussinesq system of equations, which governs buoyancy-driven ‡ows of viscous, incompressible ‡uids. This modi…cation is motivated by unresolved issues regarding the global solvability of the classical system in situations where viscous heating cannot be neglected. A simple model problem leads to a coupled system of two parabolic equations...

In this paper, a class of coupled Riccati equations by using some special solutions of nonlinear coupled Schrodinger-KdV equations of a number of exact analytical group, obtain the precise solution and two groups of new solitary wave solutions of the equations and several general forms. With the help of computer symbolic computation technology, using Fexpansion method to obtain exact solutions ...