Minimal $L^3$-initial data for potential 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.

16 pages, submitted;small typos corrected;remark below lemma 2.2 fixed

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