Error estimate of a consistent splitting GSAV scheme for the Navier-Stokes equations

We carry out a rigorous error analysis of the first-order semi-discrete (in time) consistent splitting scheme coupled with generalized scalar auxiliary variable (GSAV) approach for Navier-Stokes equations no-slip boundary conditions. The is linear, unconditionally stable, and only requires solving sequence Poisson type at each time step. By using build-in unconditional stability GSAV approach, we derive optimal global (resp. local) in estimates two three) dimensional case velocity pressure approximations.