If a= v.dv/dt then if v=0 is a also 0 but I have seen cases when a is zero but v is not

Dear Student,
First of all a=vdv/dx and not vdv/dt
dv/dt=a.

next, acceleration is defined as rate of change of velocity with respect to time. So, if the change in velocity is 0 the acceleration is 0. Rate of change in velocity can happen when:
Case1: The case you stated. v=0
Case2: Constant velocity. V will have some value > 0 but not change with time.