  Reaction-diffusion systems, which consist of the reacting particles subject
to diffusion process, constitute one of the common examples of non-linear
statistical systems. In low space dimensions $d \leq 2$ the usual description
by means of kinetic rate equations is not sufficient and the effect of density
fluctuations has to be properly taken into account. Our aim here is to analyze
a particular multi-species reaction-diffusion system characterized by reactions
$\textit{A} +\textit{A} \rightarrow (\emptyset, A),$ $\textit{A} +\textit{B}
\rightarrow \textit{A}$ at and below its critical dimension $d_c = 2$. In
particular, we investigate effect of thermal fluctuations on the reaction
kinetics, which are generated by means of random velocity field modelled by a
stochastic Navier-Stokes equations. Main theoretical tool employed is
field-theoretic perturbative renormalization group. The analysis is performed
to the first order of the perturbation scheme (one-loop approximation).
