Existence of traveling waves in the Stokes–Boussinesq system for reactive flows

We consider the Stokes–Boussinesq equations in a slanted (that is, not aligned with gravityʹs direction) cylinder of any dimension and with an arbitrary Rayleigh number. We prove the existence of a non-planar traveling wave solution, propagating at a constant speed, and satisfying the Dirichlet boundary condition in the velocity and the Neumann condition in the temperature.