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.
|Journal||Partial Differential Equations and Applications|
|Publication status||Published - 2022 Feb|
Bibliographical noteFunding Information:
We thank Professor Reinhard Farwig for valuable suggestions on Theorem . The research of Kang was partially supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350. The research of Miura was partially supported by JSPS Grant 16H06339 and 17K05312. The research of Tsai was partially supported by NSERC Grant RGPIN-2018-04137.
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis