Existence and regularity of solutions of non-Newtonian flow

The existence and regularity of Young measure-valued solutions and weak solutions to non-Newtonian flows are considered. Galerkin approximation and an L² compactness theorem are main ingredients for the proof of the existence of Young measure-valued solutions. Under a certain convexity condition for the energy, we prove that Young measure-valued solutions are weak solutions. Also, for the limited cases, we prove a regularity theorem.