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

TL;DR

This paper proves the existence of solutions to the Navier-Stokes Cauchy problem with initial data in L3 space, focusing on the conditions that guarantee a unique existence interval based on initial data properties.

Contribution

It provides a new proof of the existence of solutions in the L3 setting, emphasizing the role of initial data size and absolute continuity in the solution interval.

Findings

Existence of solutions in L3 space established.

Uniqueness of the existence interval based on initial data properties.

Conditions on initial data size and absolute continuity are crucial.

Abstract

We investigate on the existence of solutions with initial datum U0 in L3. Our chief goal is to establish the existence interval (0,T) uniquely considering the size and the absolute continuity of |U0(x)|3.