A stability result for the Stokes-Boussinesq equations in infinite 3d channels

TL;DR

This paper establishes stability estimates for the laminar front in the Stokes-Boussinesq and stationary Navier-Stokes-Boussinesq equations within a 3D channel with arbitrary Rayleigh number and specific boundary conditions.

Contribution

It provides the first uniform estimates on burning rate and flow velocity for these equations in a non-aligned, infinite 3D channel with front-like initial data.

Findings

Uniform estimates on burning rate and flow velocity derived

Stability results for laminar front established

Applicable to channels with arbitrary Rayleigh number

Abstract

We consider the Stokes-Boussinesq (and the stationary Navier-Stokes-Boussinesq) equations in a slanted, i.e. not aligned with the gravity's direction, 3d channel and with an arbitrary Rayleigh number. For the front-like initial data and under the no-slip boundary condition for the flow and no-flux boundary condition for the reactant temperature, we derive uniform estimates on the burning rate and the flow velocity, which can be interpreted as stability results for the laminar front.