IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i7p761-d528341.html
   My bibliography  Save this article

Time-Decay Estimates for Linearized Two-Phase Navier–Stokes Equations with Surface Tension and Gravity

Author

Listed:
  • Hirokazu Saito

    (Graduate School of Informatics and Engineering, The University of Electro-Communications, 5-1 Chofugaoka 1-Chome, Chofu, Tokyo 182-8585, Japan
    Partially supported by JSPS KAKENHI Grant Number JP17K14224.)

Abstract

The aim of this paper is to show time-decay estimates of solutions to linearized two-phase Navier-Stokes equations with surface tension and gravity. The original two-phase Navier-Stokes equations describe the two-phase incompressible viscous flow with a sharp interface that is close to the hyperplane x N = 0 in the N -dimensional Euclidean space, N ≥ 2 . It is well-known that the Rayleigh–Taylor instability occurs when the upper fluid is heavier than the lower one, while this paper assumes that the lower fluid is heavier than the upper one and proves time-decay estimates of L p - L q type for the linearized equations. Our approach is based on solution formulas for a resolvent problem associated with the linearized equations.

Suggested Citation

  • Hirokazu Saito, 2021. "Time-Decay Estimates for Linearized Two-Phase Navier–Stokes Equations with Surface Tension and Gravity," Mathematics, MDPI, vol. 9(7), pages 1-43, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:761-:d:528341
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/7/761/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/7/761/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:9:y:2021:i:7:p:761-:d:528341. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.