Liouville-type theorems for the stationary non-Newtonian fluids

We study Liouville-type theorems for stationary incompressible non-Newtonian fluids governed by a power-law model in R 3 . For suitable weak solutions, we establish new sufficient conditions for triviality expressed through growth bounds of the velocity in exterior annuli. Our first result extends earlier work by enlarging the admissible range of the exponent p and replacing global energy assumptions with weaker L 3 -type decay conditions. Our second result further generalizes Liouville-type criteria by allowing L q -type growth controls, which extend known results derived from mean oscillation assumptions on vector potentials. In particular, our theorems recover and extend recent Liouville results for the stationary Navier–Stokes equations as the Newtonian case.