Abstract
We are concerned with the size of the regular set for weak solutions to the Navier–Stokes equations. It is shown that if a weighted norm of initial data is finite, the suitable weak solutions are regular in a set above a space-time hypersurface determined by the degree of the weight. This result refines and generalizes Theorems C and D of Caffarelli, Kohn and Nirenberg (Comm. Pure Appl. Math. 35:6 (1982), 771–831) in various aspects. Our main tool is an -regularity theorem in terms of initial data, which is of independent interest. As applications, we also study energy concentration near a possible blow-up time and regularity for forward discretely self-similar solutions.
Citation
Kyungkeun Kang. Hideyuki Miura. Tai-Peng Tsai. "Regular sets and an -regularity theorem in terms of initial data for the Navier–Stokes equations." Pure Appl. Anal. 3 (3) 567 - 594, 2021. https://doi.org/10.2140/paa.2021.3.567
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