Mathematical modeling of rigid bodies motion through some non-Newtonian flows

The main novelty of this article is to reveal a weak formulation of rigid bodies motion arising from free boundaries evolution in visco-plastic flows governed by the incompressible Norton–Hoff operator with non-cylindrical coefficients. We supply the existence result of an interface between the two non-miscible fluids by the use of the non-smooth evolution theory. We prove that the fluid’s flow is converted to a rigid body when its viscosity is large enough. The established results are variants or extensions of the existing formulations.