1. I n t r o d u c t i o n The possibility of singularity formation from smooth initial data for the solution of the Euler equations for inviscid, incompressible fluid flow in three dimensions is one of the main unsolved problems of mathematical fluid mechanics. In spite of considerable effort on this problem from analytical, numerical and physical approaches, there is still little convincing e...

We construct the traveling wave solutions of the 1 1 -dimensional modified Benjamin-BonaMahony equation, the 2 1 -dimensional typical breaking soliton equation, the 1 1 -dimensional classical Boussinesq equations, and the 2 1 -dimensional Broer-Kaup-Kuperschmidt equations by using an extended G′/G -expansion method, where G satisfies the second-order linear ordinary differential equation. By us...

This research describes the unsteady two-dimensional reacting flows around a circular cylinder. The numerical solution combines the random vortex method for incompressible two-dimensional viscous fluid flow with a Simple Line Interface Calculation (SLIC) algorithm for the propagation of flame interface. To simplify the governing equations, two fundamental assumptions namely Low Mach Number and ...

The accurate numerical simulation of wave disturbance within harbours requires consideration of both nonlinear and dispersive wave processes in order to capture such physical effects as wave refraction and diffraction, and nonlinear wave interactions such as the generation of harmonic waves. The Boussinesq equations are the simplest class of mathematical model that contain all these effects in ...

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal tha...

In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.

This paper studies the three-dimensional density-dependent incompressible magnetohydrodynamic equations. First, a regularity criterion is proved which allows the initial density to contain vacuum. Then we establish another blow-up criterion in the Besov space Ḃ0 ∞,2 when the positive initial density is bounded away from zero. Third, we prove a global nonexistence result for initial density with...

A mathematical model for gas-liquid flows subject to mass transfer and chemical reactions is presented. It is shown that bubble-induced buoyancy resembles natural convection and can readily be incorporated into an incompressible flow solver by using an analog of the Boussinesq approximation. Extra transport equations with nonlinear source terms are introduced to describe the evolution of scalar...

Following earlier work for Stokes equations, a least-squares functional is developed for twoand three-dimensional Oseen equations. By introducing a velocity flux variable and associated curl and trace equations, ellipticity is established in an appropriate product norm. The form of Oseen equations examined here is obtained by linearizing the incompressible Navier-Stokes equations. An algorithm ...