Abstract The domain wall dynamics in the adiabatic regime has been studied. It is shown that the domain wall velocity in the low-field range (when the domain wall interacts with the distributed defects) satisfy the power law: v = S ′( H − H 0 ) β , where H 0 is the critical field. The temperature dependence of the power exponent β is treated in terms of the change of the domain wall shape from rigid to flexible one. In addition, the mobility exponent S ′ is shown to be field independent and is proportional to the domain wall mobility S in the viscous regime.