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

Kyungkeun Kang; Hideyuki Miura; Tai Peng Tsai

doi:10.1007/s42985-021-00127-2

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

Kyungkeun Kang, Hideyuki Miura, Tai Peng Tsai

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Article number	5
Journal	Partial Differential Equations and Applications
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s42985-021-00127-2
Publication status	Published - 2022 Feb

Bibliographical note

Funding 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.

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

Access to Document

10.1007/s42985-021-00127-2

Cite this

@article{b69550850e1946caa689dfbfd69f42ea,

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

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.",

author = "Kyungkeun Kang and Hideyuki Miura and Tsai, {Tai Peng}",

note = "Funding 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. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = feb,

doi = "10.1007/s42985-021-00127-2",

language = "English",

volume = "3",

journal = "Partial Differential Equations and Applications",

issn = "2662-2963",

publisher = "Springer International Publishing AG",

number = "1",

}

TY - JOUR

T1 - Local regularity conditions on initial data for local energy solutions of the Navier–Stokes equations

AU - Kang, Kyungkeun

AU - Miura, Hideyuki

AU - Tsai, Tai Peng

N1 - Funding 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. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/2

Y1 - 2022/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85126269119&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85126269119&partnerID=8YFLogxK

U2 - 10.1007/s42985-021-00127-2

DO - 10.1007/s42985-021-00127-2

M3 - Article

AN - SCOPUS:85126269119

SN - 2662-2963

VL - 3

JO - Partial Differential Equations and Applications

JF - Partial Differential Equations and Applications

IS - 1

M1 - 5

ER -

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this