  The single-species annihilation reaction $A + A \rightarrow\varnothing$ is
studied in the presence of a random velocity field generated by the stochastic
Navier-Stokes equation. The renormalization group is used to analyze the
combined influence of the density and velocity fluctuations on the long-time
behavior of the system. The direct effect of velocity fluctuations on the
reaction constant appears only from the two- loop order, therefore all stable
fixed points of the renormalization group and their regions of stability are
calculated in the two-loop approximation in the two-parameter $(\epsilon,
\Delta)$ expansion. A renormalized integro- differential equation for the
number density is put forward which takes into account the effect of density
and velocity fluctuations at next-to-leading order. Solution of this equation
in perturbation theory is calculated in a homogeneous system.
