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arXiv · 1811.00502

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

Dallas Albritton·Tobias Barker
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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 $L^3$ along a backward sequence of times.

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Dallas Albritton, Tobias Barker. 2018-11-01. On local Type I singularities of the Navier-Stokes equations and Liouville theorems. https://doi.org/10.1007/s00021-019-0448-z

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