ABSTRACT
This chapter obtains a linear system whose solution solves the time-independent incompressible Navier-Stokes system for the special case in which the external forces vector is a gradient. It develops approximate solutions for the time independent incompressible Navier-Stokes system through the generalized method of lines. The chapter recalls that for the generalized method of lines, the domain of the partial differential equation in question is discretized in lines and the concerning solution is written on these lines as functions of the boundary conditions and boundary shape. It also emphasizes that main results of the Navier-Stokes system are established through applications of the Banach fixed point theorem.
