Partially regular weak solutions of the Navier-Stokes equations in ${\mathbb{R}}^4\times [0,\infty [$

Bian Wu

We show that for any given solenoidal initial data in $L^2$ and any solenoidal external force in $L_{\text{loc}}^q\bigcap L^{3/2}$ with $q>3$, there exist partially regular weak s…