IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v93y2001i2p241-268.html
   My bibliography  Save this article

Burgers turbulence initialized by a regenerative impulse

Author

Listed:
  • Winkel, Matthias

Abstract

In this article we look at a one-dimensional infinitesimal particle system governed by the completely inelastic collision rule. Considering uniformly spread mass, we feed the system with initial velocities, so that when time evolves the corresponding velocity field fulfils the inviscid Burgers equation. More precisely, we suppose here that the initial velocities are zero, except for particles located on a stationary regenerative set for which the velocity is some given constant number. We give results of a large deviation type. First, we estimate the probability that a typical particle is located at time 1 at distance at least D from its initial position, when D tends to infinity. Its behaviour is related to the left tail of the gap measure of the regenerative set. We also show the same asymptotics for the tail of the shock interval length distribution. Second, we analyse the event that a given particle stands still at time T as T tends to infinity. The data to which we relate its behaviour are the right tail of the gap measure of the regenerative set. We conclude with some results on the shock structure.

Suggested Citation

  • Winkel, Matthias, 2001. "Burgers turbulence initialized by a regenerative impulse," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 241-268, June.
  • Handle: RePEc:eee:spapps:v:93:y:2001:i:2:p:241-268
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(00)00098-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Raphaël Lachièze-Rey, 2012. "Concave Majorant of Stochastic Processes and Burgers Turbulence," Journal of Theoretical Probability, Springer, vol. 25(2), pages 313-332, June.

    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:eee:spapps:v:93:y:2001:i:2:p:241-268. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.