Publication at Faculty of Mathematics and Physics |

2019

We deal with flows of non-Newtonian fluids in three-dimensional setting subjected to the homogeneous Dirichlet boundary condition. Under the natural monotonicity, coercivity and growth condition on the Cauchy stress tensor expressed by a power index p >= 11/5, we establish regularity properties of a solution with respect to time variable.

Consequently, we can use this better information for showing the uniqueness of the solution provided that the initial data are good enough for all power-law indices p >= 11/5. Such a result was available for p >= 12/5 and therefore the paper fills the gap and extends the uniqueness result to the whole range of p's for which the energy equality holds.