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arXiv · 2006.13145

An $\epsilon$-regularity criterion and estimates of the regular set for Navier-Stokes flows in terms of initial data

Kyungkeun Kang·Hideyuki Miura·Tai-Peng Tsai
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Abstract

We prove an $\epsilon$-regularity criterion for the 3D Navier-Stokes equations in terms of initial data. It shows that if a scaled local $L^2$ norm of initial data is sufficiently small around the origin, a suitable weak solution is regular in a set enclosed by a paraboloid started from the origin. The result is applied to the estimate of the regular set for local energy solutions with initial data in weighted $L^2$ spaces. We also apply this result to studying energy concentration near a possible blow-up time and regularity of forward discretely self-similar solutions.

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Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai. 2020-06-23. An $\epsilon$-regularity criterion and estimates of the regular set for Navier-Stokes flows in terms of initial data. https://doi.org/10.2140/paa.2021.3.567

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