Vol. 3, No. 3, 2021
Download this article
Download this article For screen
For printing
Recent Issues
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2578-5885
ISSN (print): 2578-5893
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Regular sets and an $\epsilon$-regularity theorem in terms of initial data for the Navier–Stokes equations

Kyungkeun Kang, Hideyuki Miura and Tai-Peng Tsai
Vol. 3 (2021), No. 3, 567–594
DOI: 10.2140/paa.2021.3.567
Abstract

We are concerned with the size of the regular set for weak solutions to the Navier–Stokes equations. It is shown that if a weighted L2 norm of initial data is finite, the suitable weak solutions are regular in a set above a space-time hypersurface determined by the degree of the weight. This result refines and generalizes Theorems C and D of Caffarelli, Kohn and Nirenberg (Comm. Pure Appl. Math. 35:6 (1982), 771–831) in various aspects. Our main tool is an 𝜖-regularity theorem in terms of initial data, which is of independent interest. As applications, we also study energy concentration near a possible blow-up time and regularity for forward discretely self-similar solutions.

PDF Access Denied

We have not been able to recognize your IP address 3.138.200.66 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
Navier–Stokes equations, $\epsilon$-regularity, regular set, energy concentration, discretely self-similar solutions
Mathematical Subject Classification
Primary: 35Q30, 76D05, 76D03
Milestones
Received: 20 November 2020
Revised: 8 June 2021
Accepted: 21 August 2021
Published: 24 October 2021
Authors
Kyungkeun Kang
Department of Mathematics
Yonsei University
Seoul
South Korea
Hideyuki Miura
Department of Mathematical and Computing Science
Tokyo Institute of Technology
Tokyo
Japan
Tai-Peng Tsai
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada