On Critical Spaces for the Navier–Stokes Equations

On Critical Spaces for the Navier–Stokes Equations The abstract theory of critical spaces developed in Prüss and Wilke (J Evol Equ, 2017. doi: 10.1007/s00028-017-0382-6 ), Prüss et al. (Critical spaces for quasilinear parabolic evolution equations and applications, 2017) is applied to the Navier–Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the $$L_p$$ L p – $$L_q$$ L q setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an $$\mathcal {H}^\infty $$ H ∞ -calculus with $$\mathcal {H}^\infty $$ H ∞ -angle 0, and the real and complex interpolation spaces of these operators are identified. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

On Critical Spaces for the Navier–Stokes Equations

Loading next page...
 
/lp/springer_journal/on-critical-spaces-for-the-navier-stokes-equations-h0V0VGiMur
Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-017-0342-5
Publisher site
See Article on Publisher Site

Abstract

The abstract theory of critical spaces developed in Prüss and Wilke (J Evol Equ, 2017. doi: 10.1007/s00028-017-0382-6 ), Prüss et al. (Critical spaces for quasilinear parabolic evolution equations and applications, 2017) is applied to the Navier–Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the $$L_p$$ L p – $$L_q$$ L q setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an $$\mathcal {H}^\infty $$ H ∞ -calculus with $$\mathcal {H}^\infty $$ H ∞ -angle 0, and the real and complex interpolation spaces of these operators are identified.

Journal

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Oct 5, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off