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

Kyungkeun Kang, Hideyuki Miura, Tai Peng Tsai

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1 Citation (Scopus)

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 L2 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.

Original languageEnglish
Article number5
JournalPartial Differential Equations and Applications
Volume3
Issue number1
DOIs
Publication statusPublished - 2022 Feb

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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