Skip to main content
SpringerLink
Log in

Weighted L 2-spaces and Strong Solutions of the Navier-Stokes Equations in

  • Conference paper
Trends in Partial Differential Equations of Mathematical Physics

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 61))

Abstract

We consider the velocity field u(x, t) of a Navier-Stokes flow in the whole space.

We give a persistence result in a subspace of L 2(, (1 + |x|2)5/2 dx), which allows us to fill the gap between previously known results in the weighted-L 2 setting and those on the pointwise decay of u at infinity.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Amrouche, V. Girault, M.E. Schonbek, T.P. Schonbek Pointwise Decay of Solutions and of higher derivatives to Navier-Stokes Equations, SIAM J. Math. Anal., 31, N. 4, 740–753, (2000).

    Article  MATH  MathSciNet  Google Scholar 

  2. G. Bourdaud, Localisation et multiplicateurs des espaces de Sobolev homogènes, Manuscripta Mathematica, 60, 93–130 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  3. L. Brandolese, Y. Meyer, On the instantaneous spreading for the Navier-Stokes system in the whole space, ESAIM Contr. Optim. Calc. Var. 8, 273–285 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Coifman, P.-L. Lions, Y. Meyer, S. Semmes, Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72, 247–286 (1993).

    MATH  MathSciNet  Google Scholar 

  5. S.Y. Dobrokhotov, A.I. Shafarevich, Some Integral Identities and Remarks on the Decay at Infinity of the Solutions to the Navier-Stokes Equations in the Entire Space, Russ. J. Math. Phys. Vol. 2, N. 1, 133–135 (1994).

    MATH  MathSciNet  Google Scholar 

  6. R. Farwing, H. Sohr, Weighted energy inequalities for the Navier-Stokes equations in exterior domains. Appl. Analysis 58 N.1–2, 157–173 (1995).

    Article  Google Scholar 

  7. R. Farwing, H. Sohr, Global estimates in weighted spaces of weak solutions of the Navier-Stokes equations in exterior domains, Arch. Math. 67, 319–330 (1996).

    Article  Google Scholar 

  8. G. Furioli, E. Terraneo, Molecules of the Hardy space and the Navier-Stokes equations, Funkcial. Ekvac. 45, N. 1 141–160 (2002).

    MATH  MathSciNet  Google Scholar 

  9. C. He, The Cauchy problem for the Navier-Stokes equations, J. Math. Analysis Appl. 209, 422–444 (1998).

    Google Scholar 

  10. C. He, Z. Xin, On the decay properties of Solutions to the nonstationary Navier-Stokes Equations in , Proc. Roy. Edinburgh Soc. Sect. A, 131, N. 3, 597–619 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  11. P.G. Lemarié-Rieusset, Recent developments in the Navier-Stokes problem, Chapman & Hall, CRC Press Boca Raton (2002).

    Google Scholar 

  12. T. Miyakawa, Application of Hardy Space Techniques to the Time-Decay Problem for Incompressible Navier-Stokes Flows in , Funkcial. Ekvac., 41, 383–434 (1998).

    MATH  MathSciNet  Google Scholar 

  13. T. Miyakawa, On space time decay properties of nonstationary incompressible Navier-Stokes flows in , Funkcial. Ekvac., 32, N. 2, 541–557 (2000).

    MathSciNet  Google Scholar 

  14. M.E. Schonbek, T.P. Schonbek, On the boundedness and decay of moments of so-lutions of the Navier-Stokes equations, Advances in Diff. Eq., 7–9 July–September (2000).

    Google Scholar 

  15. F. Vigneron, Ph. D Dissertation, Ecole polytechnique, Palaiseau (France), in preparation.

    Google Scholar 

  16. A. Youssfi, Localisation des espaces de Besov homogènes, Indiana Univ. Math. J., 37, 565–587 (1988).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut Girard Desargues, Université Claude Bernard Lyon 1, 21, avenue Claude Bernard, F-69622, Villeurbanne Cedex, France

    Lorenzo Brandolese

Authors
  1. Lorenzo Brandolese
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Universidade de Lisboa/CMAF, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal

    José Francisco Rodrigues

  2. Steklov Institute of Mathematics, Russian Academy of Science, 27, Fontanka, St. Petersburg, 191023, Russia

    Gregory Seregin

  3. Departamento de Matemática, Universidade de Coimbra/FCT, Apartado 3008, 3001-454, Coimbra, Portugal

    José Miguel Urbano

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Brandolese, L. (2005). Weighted L 2-spaces and Strong Solutions of the Navier-Stokes Equations in . In: Rodrigues, J.F., Seregin, G., Urbano, J.M. (eds) Trends in Partial Differential Equations of Mathematical Physics. Progress in Nonlinear Differential Equations and Their Applications, vol 61. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7317-2_3

Download citation

Publish with us

Policies and ethics

Search

Navigation