  Using analogies between flow equations from the Functional Renormalization
Group and flow equations from (numerical) fluid dynamics we investigate the
effects of bosonic fluctuations in a bosonized Gross-Neveu model -- namely the
Gross-Neveu-Yukawa model. We study this model for finite numbers of fermions at
varying chemical potential and temperature in the local potential
approximation. Thereby we numerically demonstrate that for any finite number of
fermions and as long as the temperature is non-zero, there is no $\mathbb{Z}_2$
symmetry breaking for arbitrary chemical potentials.
