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arXiv · 2302.06509

Blow-up of dynamically restricted critical norms near a potential Navier-Stokes singularity

Tobias Barker·Pedro Gabriel Fernández-Dalgo·Christophe Prange
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Abstract

In this paper we develop new methods to obtain regularity criteria for the three-dimensional Navier-Stokes equations in terms of dynamically restricted endpoint critical norms: the critical Lebesgue norm in general or the critical weak Lebesgue norm in the axisymmetric case. This type of results is inspired in particular by a work of Neustupa (2014), which handles certain non endpoint critical norms. Our work enables to have a better understanding of the nonlocal effect of the pressure on the regularity of the solutions.

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Tobias Barker, Pedro Gabriel Fernández-Dalgo, Christophe Prange. 2023-02-13. Blow-up of dynamically restricted critical norms near a potential Navier-Stokes singularity. https://arxiv.org/abs/2302.06509

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