Context :

Aims : We aim to investigate the relation between the long-term flux density and the position angle ( PA ) evolution of inner-jet in blazars .

Methods : We have carried out the elliptic Gaussian model-fit to the ‘ core ’ of 50 blazars from 15 GHz VLBA data , and analyzed the variability properties of three blazars from the model-fit results .

Results : Diverse correlations between the long-term peak flux density and the PA evolution of the major axis of the ‘ core ’ have been found in \sim 20 % of the 50 sources .
Of them , three typical blazars have been analyzed , which also show quasi-periodic flux variations of a few years ( T ) .
The correlation between the peak flux density and the PA of inner-jet is positive for S5 0716+714 , and negative for S4 1807+698 .
The two sources can not be explained with the ballistic jet models , the non-ballistic models have been analyzed to explain the two sub-luminal blazars .
A correlation between the peak flux density and the PA ( with a T/4 time lag ) of inner-jet is found in [ HB89 ] 1823+568 , this correlation can be explained with a ballistic precession jet model .
All the explanations are based mainly on the geometric beaming effect ; physical flux density variations from the jet base would be considered for more complicated situations in future , which could account for the no or less significance of the correlation between the peak flux density and the PA of inner-jet in the majority blazars of our sample .

Conclusions :