We study the Oberbeck-Boussinesq approximation describing the motion of an incompressible, heat-conducting fluid occupying a general unbounded domain in R3. We provide a rigorous justification of the model by means of scale analysis of the full Navier-Stokes-Fourier system in the low Mach and Froude number regime on large domains, the diameter of which is proportional to the speed of sound. Fin...

Considered here are Boussinesq systems of equations of surface water wave theory over a variable bottom. A simplified such Boussinesq system is derived and solved numerically by the standard Galerkin-finite element method. We study by numerical means the generation of tsunami waves due to bottom deformation and we compare the results with analytical solutions of the linearized Euler equations. ...

An implicit procedure based on the artificial compressibility formulation is presented for the numerical solution of the two-dimensional incompressible steady Navier-Stokes equations

The Navier–Stokes equations for incompressible flows past a two–dimensional sphere are considered in this article. The existence of an inertial form of the equations is established. Furthermore for the first time for fluid equations, we derive an upper bound on the dimension of the differential system (inertial manifold) which fully reproduces the infinite dimensional dynamics. This bound is ex...

We study the flow of an incompressible viscous fluid through a long tube with compliant walls. The flow is governed by a given time dependent pressure head difference. The Navier-Stokes equations for an incompressible viscous fluid are used to model the flow, and the Navier equations for a curved, linearly elastic membrane to model the wall. Employing the asymptotic techniques typically used in...

We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type equations, follow from the present model for...

This paper is concerned with the global regularity of two-dimensional generalized Boussinesq equations. When dissipation mechanism only fractional vertical in horizontal velocity and velocity, it examined that system has a unique smooth solution. The finding not settles problem remarked (J. Differential Equations 268: 910–944, 2020), but also relaxes restriction on initial data.