  We investigate a system describing the flow of a compressible two-component
mixture. The system is composed of the compressible Navier-Stokes equations
coupled with non-symmetric reaction-diffusion equations describing the
evolution of fractional masses. We show the local existence and, under certain
smallness assumptions, also the global existence of unique strong solutions in
$L_p-L_q$ framework. Our approach is based on so called entropic variables
which enable to rewrite the system in a symmetric form. Then, applying
Lagrangian coordinates, we show the local existence of solutions applying the
$L_p$-$L_q$ maximal regularity estimate. Next, applying exponential decay
estimate we show that the solution exists globally in time provided the initial
data is sufficiently close to some constants. The nonlinear estimates impose
restrictions $2<p<\infty, \ 3<q<\infty$. However, for the purpose of generality
we show the linear estimates for wider range of $p$ and $q$.
