On local type I singularities of the Navier-Stokes equations and Liouville theorems

Tobias Barker, Dallas Albritton

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4 Citations (SciVal)

Abstract

We prove that suitable weak solutions of the Navier–Stokes equations exhibit Type I singularities if and only if there exists a non-trivial mild bounded ancient solution satisfying a Type I decay condition. The main novelty is in the reverse direction, which is based on the idea of zooming out on a regular solution to generate a singularity. By similar methods, we prove a Liouville theorem for ancient solutions of the Navier–Stokes equations bounded in L3 along a backward sequence of times.
Original languageEnglish
JournalJournal of Mathematical Fluid Mechanics
Volume21
Issue number43
DOIs
Publication statusPublished - 8 Jul 2019

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