Uniqueness of solutions to to Navier Stokes equation with small initial data in $L^{3,\infty}(R^3)$

TL;DR

This paper proves the uniqueness of solutions to the Navier-Stokes equations when the initial data is small in the Lorentz space $L^{3, abla}(R^3)$, addressing a previously raised open problem.

Contribution

It establishes the first proof of uniqueness for Navier-Stokes solutions with small initial data in the Lorentz space $L^{3, abla}(R^3)$.

Findings

Proves uniqueness of Navier-Stokes solutions with small initial data in $L^{3, abla}(R^3)$

Addresses an open problem from prior literature

Contributes to understanding solution behavior in Lorentz spaces

Abstract

In this short note we address a problem raised in [21], concerning the uniqueness of solutions to Naiver Stokes equation with small initial data in $L^{3,\infty}(R^3)$, the Lorentz space. We prove uniqueness for such initial data.