English

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

Analysis of PDEs 2021-06-09 v1

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 L2L^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, Kohn and Nirenberg (Comm. Pure Appl. Math. 35; 1982) and our recent paper [15] as well.

Keywords

Cite

@article{arxiv.2106.03980,
  title  = {Local regularity conditions on initial data for local energy solutions of the Navier-Stokes equations},
  author = {Kyungkeun Kang and Hideyuki Miura and Tai-Peng Tsai},
  journal= {arXiv preprint arXiv:2106.03980},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:2006.13145