Existence and regularity of solutions of non-Newtonian flow

The existence and regularity of Young measure-valued solutions and weak sol utions to non-Newtonian flows are considered. Galerkin approximation and an L-2 compactness theorem are main ingredients for the proof of the existenc e of Young measure-valued solutions. Under a certain convexity condition fo r the energy, we prove that Young measure-valued solutions are weak solutio ns. Also, for the limited cases, we prove a regularity theorem.