EQUIVALENCE OF U-P AND ZETA-PSI-FORMULATIONS OF THE TIME-DEPENDENT NAVIER-STOKES EQUATIONS

This paper deals with the non-stationary incompressible Navier-Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously , by virtue of a condition of compatibility between the boundary and i nitial values of the normal component of velocity. This condition is s hown to be the only compatibility condition necessary to allow for sol utions of a minimal regularity, namely H-1 for the velocity, as in mos t current numerical schemes relying on spatial discretizations of loca l type.