Vol. 3, No. 3, 2021

Download this article
Download this article For screen
For printing
Recent Issues
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
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
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.
Navier–Stokes regularity criteria in sum spaces

Evan Miller

Vol. 3 (2021), No. 3, 527–566
DOI: 10.2140/paa.2021.3.527

We will consider regularity criteria for the Navier–Stokes equation in mixed Lebesgue sum spaces. In particular, we will prove regularity criteria that only require control of the velocity, vorticity, or the positive part of the second eigenvalue of the strain matrix, in the sum space of two scale-critical spaces. This represents a significant step forward, because each sum-space regularity criterion covers a whole family of scale-critical regularity criteria in a single estimate. In order to show this, we will also prove a new inclusion and inequality for sum spaces in families of mixed Lebesgue spaces with a scale invariance that is also of independent interest.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address 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:

Mathematical Subject Classification
Primary: 35Q30
Received: 26 September 2020
Revised: 4 June 2021
Accepted: 21 August 2021
Published: 24 October 2021
Evan Miller
Department of Mathematics and Statistics
McMaster University
Hamilton, ON