Vol. 296, No. 1, 2018

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Vol. 293: 1  2
Vol. 292: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Other MSP Journals
This article is available for purchase or by subscription. See below.
Besov-weak-Herz spaces and global solutions for Navier–Stokes equations

Lucas C. F. Ferreira and Jhean E. Pérez-López

Vol. 296 (2018), No. 1, 57–77

We consider the incompressible Navier-Stokes equations (NS) in n for n 2. Global well-posedness is proved in critical Besov-weak-Herz spaces (BWH-spaces) that consist in Besov spaces based on weak-Herz spaces. These spaces are larger than some critical spaces considered in previous works for NS. For our purposes, we need to develop a basic theory for BWH-spaces containing properties and estimates such as heat semigroup estimates, embedding theorems, interpolation properties, among others. In particular, we prove a characterization of Besov-weak-Herz spaces as interpolation of Sobolev-weak-Herz ones, which is key in our arguments. Self-similarity and asymptotic behavior of solutions are also discussed. Our class of spaces and its properties developed here could also be employed to study other PDEs of elliptic, parabolic and conservation-law type.

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:

Navier–Stokes equations, well-posedness, Besov-weak-Herz spaces, interpolation, heat semigroup estimates, self-similarity
Mathematical Subject Classification 2010
Primary: 35A23, 35K08, 42B35, 76D03, 76D05
Secondary: 35C06, 35C15, 46B70
Received: 23 April 2017
Accepted: 9 January 2018
Published: 1 May 2018
Lucas C. F. Ferreira
Departamento de Matemática
Universidade Estadual de Campinas, IMECC
Jhean E. Pérez-López
Escuela de Matemáticas
Universidad Industrial de Santander