IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-030-15242-0_11.html
   My bibliography  Save this book chapter

Mathematical Theory of Incompressible Flows: Local Existence, Uniqueness, and Blow-Up of Solutions in Sobolev–Gevrey Spaces

In: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Author

Listed:
  • Wilberclay G. Melo

    (Universidade Federal de Sergipe, Departamento de Matemática)

  • Natã Firmino Rocha

    (Universidade Federal de Minas Gerais, Departamento de Matemática)

  • Ezequiel Barbosa

    (Universidade Federal de Minas Gerais, Departamento de Matemática)

Abstract

This work establishes the local existence and uniqueness as well as the blow-up criteria for solutions of the Navier–Stokes equations in Sobolev–Gevrey spaces. More precisely, if the maximal time of existence of solutions for these equations is finite, we demonstrate the explosion, near this instant, of some limits superior and integrals involving a specific usual Lebesgue spaces and, as a consequence, we prove the lower bounds related to Sobolev–Gevrey spaces.

Suggested Citation

  • Wilberclay G. Melo & Natã Firmino Rocha & Ezequiel Barbosa, 2019. "Mathematical Theory of Incompressible Flows: Local Existence, Uniqueness, and Blow-Up of Solutions in Sobolev–Gevrey Spaces," Springer Books, in: Hemen Dutta & Ljubiša D. R. Kočinac & Hari M. Srivastava (ed.), Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, chapter 0, pages 311-349, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15242-0_11
    DOI: 10.1007/978-3-030-15242-0_11
    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:978-3-030-15242-0_11. 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.