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.

Abstract We present the first simulations of a reduced magnetized plasma model that incorporates both arbitrary wavelength polarization and non-Oberbeck–Boussinesq effects. Significant influence these two effects on density, electric potential <mml:mi mathvariant="bold-ital...

In order to investigate corrections to the common KdV approximation to long waves, we derive modulation equations for the evolution of long wavelength initial data for a Boussinesq equation. The equations governing the corrections to the KdV approximation are explicitly solvable and we prove estimates showing that they do indeed give a significantly better approximation than the KdV equation al...