Pulsating Fronts in a 2D Reactive Boussinesq System

TL;DR

This paper proves the existence of smooth pulsating front solutions with positive speed in a 2D reactive Boussinesq system, coupling reaction-diffusion and fluid flow equations under specific boundary conditions.

Contribution

It introduces the first proof of pulsating front solutions in a 2D reactive Boussinesq system with no stress boundary conditions.

Findings

Existence of smooth pulsating fronts with positive speed

Coupling of reaction-advection-diffusion with Navier-Stokes equations

Analysis under periodic, unbounded domain conditions

Abstract

We consider a reactive Boussinesq system with no stress boundary conditions in a periodic domain which is unbounded in one direction. Specifically, we couple the reaction-advection-diffusion equation for the temperature, $T$, and the linearized Navier-Stokes equation with the Boussinesq approximation for the fluid flow, $u$. We show that this system admits smooth pulsating front solutions that propagate with a positive, fixed speed.