Smooth Solutions of the Navier-Stokes Equation

Abstract

Smooth solutions of the Navier-Stokes equation with smooth but otherwise unconstrained initial conditions are constructed, to solve the Millennium fluids problem in the positive. The smooth solutions are the mean values of general weak solutions and are alternately characterized as the entropy production minimizing solutions. The construction occurs in a finite periodic cube.

arXiv commentThis paper is merged with "Non-Smooth Solutions of the Navier-Stokes Equation" [arXiv:2410.09261 ]; identification of solution of Millennium Fluids prize corrected and with minor rewriting