  We use the renormalization group method to study model E of critical dynamics
in the presence of velocity fluctuations arising in accordance with the
stochastic Navier-Stokes equation. Using Martin-Siggia-Rose theorem, we obtain
a field- theoretical model that allows a perturbative renormalization group
analysis. By direct power counting and an analysis of ultraviolet divergences,
we show that the model is multiplicatively renormalizable, and we use a
two-parameter expansion in $\varepsilon$ and $\delta$ to calculate
renormalization constants. Here, $\varepsilon$ is a deviation from the critical
dimension four, and $\delta$ is a deviation from the Kolmogorov regime. We
present the results of the one-loop approximation and part of the fixed-point
structure. We briefly discuss the possible effect of velocity fluctuations on
the large-scale behavior of the model.
