A new proof of existence in the 𝐿³-setting of solutions to the Navier–Stokes Cauchy problem

We investigate the existence of solutions with initial datum $U\_0$ in $L^3$. Our main goal is to establish the existence interval $(0, T)$, uniquely considering the size ${||U\_0||}\_3$ and the absolute continuity of ${|U\_0(x)|}^3$.