Chemically Reacting Fluid Flows: Weak Solutions and Global Attractors

In this paper we present a model for incompressible chemically reacting flows where reactants enter the domain, react, and then leave the domain. In the interior of the domain we have the Navier–Stokes equations for the fluid flow coupled with reaction diffusion equations for the chemistry and temperature. On the boundary we use mixed Neumann and inhomogeneous Robin boundary conditions for the chemistry and temperature equations which fix the amount of chemicals and heat flowing into the system. For three dimensional domains we then show the existence of weak solutions which are physically reasonable, i.e., which satisfy certain maximum principle properties. These solutions are sufficient to provide the basis for a dynamical systems study of these reacting flows. We do not show that the solutions are unique; however, we are able to show the existence of global attractors for the system