# A new proof of existence in the $L^3$-setting of solutions to the Navier–Stokes Cauchy problem

• ### Francesca Crispo

Università degli Studi della Campania “L. Vanvitelli”, Caserta, Italy

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## Abstract

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 ${|U_0(x)|}^3$.