Abraham and Minkowski momenta in the optically induced motion of fluids

Does the Abraham or the Minkowski momentum describe the momentum transport of light in media? Here we show that this is a question of fluid dynamics. In momentum transport, neither the Abraham nor the Minkowski momentum is fundamental, but they emerge depending on the fluid-mechanical response of the medium on the light. If the fluid is not brought into motion, the Minkowski momentum emerges, if it moves the Abraham momentum appears.