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

Author

Listed:
  • Kyungkeun Kang

    (Yonsei University)

  • Hideyuki Miura

    (Tokyo Institute of Technology)

  • Tai-Peng Tsai

    (University of British Columbia)

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.

Suggested Citation

  • Kyungkeun Kang & Hideyuki Miura & Tai-Peng Tsai, 2022. "Local regularity conditions on initial data for local energy solutions of the Navier–Stokes equations," Partial Differential Equations and Applications, Springer, vol. 3(1), pages 1-19, February.
    • Handle: RePEc:spr:pardea:v:3:y:2022:i:1:d:10.1007_s42985-021-00127-2
    DOI: 10.1007/s42985-021-00127-2
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