IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-04068-9_20.html
   My bibliography  Save this book chapter

Small Perturbations of Initial Conditions of Solutions of the Navier–Stokes Equations in the L3–Norm and Applications

In: Advances in Mathematical Fluid Mechanics

Author

Listed:
  • Petr Kučera

    (Czech Technical University, Department of Mathematics, Faculty of Civil Engineering)

Abstract

In this paper, we solve two problems. We prove a theorem on stability of a strong solution with respect to the norm ║ ⋅ ║L2 +║⋅ ║L3 in Sect. 2. Then, in Sect.3, we show that there exist strong solutions of the Navier-Stokes initial-boundary value problem such that their initial values are arbitrarily large (in the norm of D(A¼)) and they belong to an arbitrarily chosen open set U ⊂ D(A½) at a time instant ξ > 0 which can be as small as we wish (We denote by A the Stokes operator.).

Suggested Citation

  • Petr Kučera, 2009. "Small Perturbations of Initial Conditions of Solutions of the Navier–Stokes Equations in the L3–Norm and Applications," Springer Books, in: Rolf Rannacher & Adélia Sequeira (ed.), Advances in Mathematical Fluid Mechanics, pages 319-328, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04068-9_20
    DOI: 10.1007/978-3-642-04068-9_20
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-642-04068-9_20. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.