ON VARIATIONAL PRINCIPLES FOR A NON-NEWTONIAN FLUID

For the boundary value problem for creeping flow of a fluid, called "a generalized Newtonian fluid", which is defined by the constitutive relations τij= 2η (IIε, IIIε)εij, the uniqueness of its solution are proved, and two equivalent variational problems are formulated. This fluid contains plastic fluids. The flow field, therefore, may consist of flow regions and stationary regions, or may include surfaces of discontinuous velocity. In stationary regions the stress field is not unique. Present work is a partial extention and development of studies by Hill and Prager.