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arXiv · 1804.09842

Minimal blow-up initial data in critical Fourier-Herz spaces for potential Navier-Stokes singularities

Jingyue Li·Changxing Miao·Xiaoxin Zheng
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Abstract

In this paper, we mainly prove the existence of the minimal blow-up initial data in critical Fourier-Herz space $F\dot{B}^{2-{\frac3p}}_{p,q}(\RR^3)$ with $1<p\leq\infty$ and $1\leq q<\infty$ for the three dimensional incompressible potential Navier-Stokes equations by developing techniques of "localization in space" involving the partial regularity given by the De Giorgi iteration, weak-strong uniqueness, the short-time behaviour of the kinetic energy and stability of singularity of Calder\'on's solution.

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Jingyue Li, Changxing Miao, Xiaoxin Zheng. 2018-04-26. Minimal blow-up initial data in critical Fourier-Herz spaces for potential Navier-Stokes singularities. https://arxiv.org/abs/1804.09842

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