Vol. 11, No. 6, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 8, 2619–2996
Issue 7, 2247–2618
Issue 6, 1871–2245
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
Blow-up criteria for the Navier–Stokes equations in non-endpoint critical Besov spaces

Dallas Albritton

Vol. 11 (2018), No. 6, 1415–1456
Abstract

We obtain an improved blow-up criterion for solutions of the Navier–Stokes equations in critical Besov spaces. If a mild solution u has maximal existence time T < , then the non-endpoint critical Besov norms must become infinite at the blow-up time:

limtTu( ,t)p,q1+3p(3) = ,3 < p,q < .

In particular, we introduce a priori estimates for the solution based on elementary splittings of initial data in critical Besov spaces and energy methods. These estimates allow us to rescale around a potential singularity and apply backward uniqueness arguments. The proof does not use profile decomposition.

Keywords
Navier–Stokes equations, Besov spaces, blow-up criteria
Mathematical Subject Classification 2010
Primary: 35Q30
Milestones
Received: 20 February 2017
Revised: 3 December 2017
Accepted: 14 February 2018
Published: 3 May 2018
Authors
Dallas Albritton
School of Mathematics
University of Minnesota
Minneapolis, MN
United States