Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
The Work of Yoshihiro Shibata Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Weighted L p − L q Estimates of Stokes Semigroup in Half-Space and Its Application to the Navier-Stokes Equations

Authors : Takayuki Kobayashi, Takayuki Kubo

Published in: Recent Developments of Mathematical Fluid Mechanics

Publisher: Springer Basel

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We consider the Navier-Stokes equations in half-space and in L p space with Muckenhoupt weight and show the \(L^{p} - L^{q}\) estimates of Stokes semigroup with \(\langle x'\rangle ^{s_{1}}\langle x_{n}\rangle ^{s_{n}}\) type weight. Finally as the application of the weighted \(L^{p} - L^{q}\) estimates, we shall obtain the weighted asymptotic behavior of the solution to the Navier-Stokes equations.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Stability of Time Periodic Solutions for the Rotating Navier-Stokes Equations
next chapter On Vorticity Formulation for Viscous Incompressible Flows in R + 3
Literature
1.
T. Abe, Y. Shibata, On a resolvent estimate of the Stokes equation on an infinite layer, Part 2 \(\lambda = 0\) case. J. Math. Fluid Mech. 5, 245–274 (2003)MathSciNetMATH
2.
3.
H.O. Bae, H.J. Choe, Decay rate for the incompressible flows in half space. Math. Z. 238, 799–816 (2001).MathSciNetMATH
4.
5.
W. Dan, Y. Shibata, On the L q - L r estimates of the Stokes semigroup in a two dimensional exterior domain. J. Math. Soc. Jpn. 51, 181–207 (1999)MathSciNetCrossRefMATH
6.
W. Dan, T. Kobayashi, Y. Shibata, On the local energy decay approach to some fluid flow in exterior domain, in Recent Topics on Mathematical Theory of Viscous Incompressible Fluid. Lecture Notes in Numerical and Applied Mathematics, vol.16 (Kinokuniya, Tokyo, 1998), pp. 1–51
7.
Y. Enomoto, Y. Shibata, On the rate of decay of the Ossen semigroup in exterior domains and its application to Navier-Stokes equation. J. Math. Fluid Mech. 7, 339–367 (2005)MathSciNetCrossRefMATH
8.
9.
A. Fröhlich, Helmholtz decomposition of weighted L q spaces for Muckenhoupt weights. Ann. Univ. Ferrara-Sez. VII -Sc. Mat. XLVI, 11–19 (2000)
10.
A. Fröhlich, The Stokes operator in weighted L q -spaces I: weighted estimates for the Stokes Resolvent Problem in a half-space. J. Math. Fluid Mech. 5, 166–199 (2003)MathSciNetMATH
11.
Y. Fujigaki, T. Miyakawa, Asymptotic profiles of nonstationary incompressible Navier-Stokes flows in the half-space. Methods Appl. Anal. 8(1), 121–157 (2001)MathSciNetMATH
12.
13.
H. Iwashita, L q -L r estimates for solutions of the nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problems in L q spaces. Math. Ann. 285, 265–288 (1989)MathSciNetCrossRefMATH
14.
15.
B.J. Jin, Spatial and temporal decay estimate of the Stokes flow of weighted L 1 initial data in the half-space. Nonlinear Anal. 73, 1394–1407 (2010)MathSciNetCrossRefMATH
16.
T. Kato, Strong L p -solutions of the Navier-Stokes equation in \(\mathbb{R}^{m}\), with applications to weak solutions. Math. Z. 187, 471–480 (1984)MathSciNetCrossRefMATH
17.
T. Kobayashi, T. Kubo, Weighted L p -theory for the Stokes resolvent in some unbounded domains. Tsukuba J. Math. 37(2), 179–205 (2013)MathSciNetCrossRefMATH
18.
19.
T. Kubo, Y. Shibata, On the Stokes and Navier-Stokes equations in a perturbed half-space. Adv. Differ. Equ. 10(6), 695–720 (2005)MathSciNetMATH
20.
21.
22.
E.M. Stein, Singular Integrals and Differentiability Properties of Functions (Princeton University Press, Princeton, 1970)MATH
23.
Metadata
Title
Weighted L p − L q Estimates of Stokes Semigroup in Half-Space and Its Application to the Navier-Stokes Equations
Authors
Takayuki Kobayashi
Takayuki Kubo
Copyright Year
2016
Publisher
Springer Basel
Book
Recent Developments of Mathematical Fluid Mechanics

Print ISBN: 978-3-0348-0938-2

Electronic ISBN: 978-3-0348-0939-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-0348-0939-9_18

Premium Partner

    Image Credits