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We propose a global scheme for the incompressible Navier Stokes equation,where at each time step a damping potential term is introduced via a timedilation transformation of the equation itself. This leads a global upperbounds of the value function and its spatial derivatives. The regularity islimited only by the regularity of the viscosity coefficient function and by theregularity and polynomial decay of the data. On an analytical level the schemeproposed is an alternative to schemes with external control functions.

On an auto-controlled global existence scheme of the incompressible Navier Stokes equation