|Date||Apr 13, 2017|
We are concerned with non-Newtonian Navier-Stokes equations of a power law type with an exponent q in three dimensions. We establish the local existence of regular solutions for 2 < q locally in time, if initial data is sufficiently smooth. Furthermore, if initial data is sufficiently small, the regular solutions are extended globally in time. The method of proof also works for more general type of strain tensors as long as some structure conditions as long as some structure conditions are satisfied. This is a joint work with H.-K. Kim and J.-M. Kim.