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

Francesca Crispo

doi:10.4171/esiam/3

BooksesiamCollected Volumepp. 115–134

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

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

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