Global Solutions to a Reactive Boussinesq System with Front Data on an Infinite Domain
Abstract
We prove the existence of global solutions to a coupled system of NavierStokes, and reactiondiffusion equations (for temperature and mass fraction) with prescribed front data on an infinite vertical strip or tube. This system models a onestep exothermic chemical reaction. The heat release induced volume expansion is accounted for via the Boussinesq approximation. The solutions are time dependent moving fronts in the presence of fluid convection. In the general setting, the fronts are subject to intensive RayleighTaylor and thermaldiffusive instabilities. Various physical quantities, such as fluid velocity, temperature, and front speed, can grow in time. We show that the growth is at most for large time t by constructing a nonlinear functional on the temperature and mass fraction components. These results hold for arbitrary order reactions in two space dimensions and for quadratic and cubic reactions in three space dimensions. In the absence of any thermaldiffusive instability (unit Lewis number), and with weak fluid coupling, we construct a class of fronts moving through shear flows. Although the front speeds may oscillate in time, we show that they are uniformly bounded for large t. The front equation shows the generic timedependent nature of the front speeds and the straining effect of the flow field.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1998
 DOI:
 10.1007/s002200050330
 Bibcode:
 1998CMaPh.193..287M