A multifluid model with chemically reacting components – construction of weak solutions.

We investigate the existence of weak solutions to the multi-component system, consisting of
compressible chemically reacting components, coupled with the Stokes equation for the velocity.
Specifically, we consider the case of irreversible chemical reaction and assume the nonlinear rela-
tion between the pressure and the particular densities. These assumptions cause the additional
difficulties in the mathematical analysis, due to the possible presence of vacuum.
It is shown that there exists a global weak solution, satisfying the L∞ bounds for all the compo-
nents. Moreover, despite the lack of the regularity on the gradients, we obtain strong compactness
of densities in L2. The applied method captures the properties of the models of high generality,
which admit an arbitrary number of components. Furthermore, the framework we develop can
handle models that contain both diffusing and non-diffusing elements.