Local regularity conditions on initial data for local energy solutions of the Navier–Stokes equations

Kyungkeun Kang (), Hideyuki Miura () and Tai-Peng Tsai ()
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Kyungkeun Kang: Yonsei University
Hideyuki Miura: Tokyo Institute of Technology
Tai-Peng Tsai: University of British Columbia

Partial Differential Equations and Applications, 2022, vol. 3, issue 1, 1-19

Abstract: Abstract We study the regular sets of local energy solutions to the Navier–Stokes equations in terms of conditions on the initial data. It is shown that if a weighted $$L^2$$ L 2 norm of the initial data is finite, then all local energy solutions are regular in a region confined by space-time hypersurfaces determined by the weight. This result refines and generalizes Theorems C and D of Caffarelli et al. (Comm. Pure Appl. Math. 35(6):771–831, 1982) and our recent paper (Kang et al., Pure Appl. Anal. arXiv:2006.13145 ) as well.

Keywords: Navier–Stokes equations; Regular sets; Local energy solutions; 35Q30; 76D05; 76D03 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-021-00127-2

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