The Time Fractional Navier-Stokes-Damped Equations with Slip Boundary Conditions

In this paper, an initial boundary value problem for the time fractional Navier-Stokes-Damped equations with a Navier-type slip boundary condition is considered. The existence, uniqueness and regularity of the solutions to the time fractional Navier-Stokes-Damped equations with slip boundary conditions are investigated. Firstly, the existence of weak solutions for \(\beta \ge 1\) is established using the Galerkin approximation. Secondly, it is demonstrated that for \(\beta \ge 4\) , the weak solution becomes unique. Lastly, the regularity of the solution for \(\beta \ge 1 + 2\alpha \) is proven.