Minimal $L^3$-initial data for potential Navier-Stokes singularities

TL;DR

This paper presents a straightforward proof demonstrating the existence of initial data with minimal L^3 norm that can lead to potential singularities in the Navier-Stokes equations, building on recent foundational work.

Contribution

It introduces a simplified proof using splitting and energy methods for the existence of minimal L^3 initial data associated with potential Navier-Stokes singularities.

Findings

Established existence of minimal L^3 initial data for potential singularities

Provided a simpler proof compared to previous profile decomposition techniques

Enhanced understanding of initial conditions leading to Navier-Stokes singularities

Abstract

We give a simple proof of the existence of initial data with minimal $L^3$ norm for potential Navier-Stokes singularities, recently established in (arXiv:1012.0145v2) with techniques based on profile decomposition. Our method is based on suitable splittings and energy methods.