Global in time solution to the incompressible Navier-Stokes equations on $\Real^n$. An Elementary Approach

Abstract

In this paper we prove a theorem of global time-extension for the local classical solution of Navier-Stokes's evolution problem in $\Real^n$ with $n\geqslant2$ for incompressible fluids subjected to external forces and regular initial conditions. This will be achieved by expressing the boundedness of the time derivative of the $L^\infty$ solution norm.