On the motion of several rigid bodies in an incompressible non-Newtonian fluid

The global existence of weak solutions is proved for the problem of the motion of one or several rigid bodies immersed in a non-Newtonian fluid of power-law type. The result is based on the fact that possible collisions of two rigid objects are outset by the phenomenon of shear thickening. The key ingredient of the proof is the strong convergence of the velocity gradients achieved by means of the method of pressure localization.