ON SOLUTIONS TO THE TIME-FRACTIONAL NAVIER–STOKES EQUATIONS WITH DAMPING

We deal with the time-fractional Navier–Stokes equations with damping in a bounded domain Ω in ℝ3. First, we establish the existence of weak solutions by Galerkin approximation for β≥1. We also show the uniqueness of weak solutions for β≥4. Further, we prove the regularity of the solution for β≥3 and 4βμ>1.