On the periodic Navier--Stokes equation: An elementary approach to existence and smoothness for all dimensions $n\ge 2$

Philipp J. di Dio

In this paper we study the periodic Navier--Stokes equation. From the periodic Navier--Stokes equation and the linear equation ${\partial }_{t}u=\nu \Delta u+\mathbb{P}[v\nabla u]$ we deri…