SOLUTIONS FOR INCOMPRESSIBLE NON-NEWTONIAN FLUIDS

For the model of a viscous incompressible fluid, where the viscous str ess tensor satisfies the growth condition \tau(ij) (e)\ less-than-or-e qual-to C (1 + Absolute value of e)p-1, with e the rate of strain tens or. We prove the existence of Young measure valued solutions for p > 1 if n = 2, and for p > 6/5 if n = 3; the existence of weak solutions f or p > 3/2 if n = 2, and for p > 9/5 if n = 3, and the existence of un ique regular weak solutions for p greater-than-or-equal-to 2 if n = 2, and for p greater-than-or-equal-to 11/5 if n = 3. The analysis deals with the associated space periodic problem.