IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v31y1989i1p1-31.html
   My bibliography  Save this article

Stochastic flows with stationary distribution for two-dimensional inviscid fluids

Author

Listed:
  • Albeverio, Sergio
  • Høegh-Krohn, Raphael

Abstract

We consider the Euler equation for an incompressible fluid in a general bounded domain of 2 with stochastic initial data. Extending previous work (for a fluid in a periodic box) we prove that the distribution of velocities u given as the standard normal distribution [mu][beta][gamma] with respect to the quadratic form [gamma]S(u) + [beta]H(u), with [beta], [gamma] >= 0, S, H being respectively the entropy and energy, is infinitesimally invariant with respect to the dynamics given by the Euler equation, in the sense that there is a one parameter group of unitary operators in L2([mu][beta][gamma]) with generator coinciding on a dense domain with the Liouville operator associated to the Euler flow. We also mention problems connected with proving the global invariance and the uniqueness of the stochastic flow.

Suggested Citation

  • Albeverio, Sergio & Høegh-Krohn, Raphael, 1989. "Stochastic flows with stationary distribution for two-dimensional inviscid fluids," Stochastic Processes and their Applications, Elsevier, vol. 31(1), pages 1-31, March.
    • Handle: RePEc:eee:spapps:v:31:y:1989:i:1:p:1-31
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(89)90100-2
    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. Albeverio, S. & Barbu, V. & Ferrario, B., 2008. "Uniqueness of the generators of the 2D Euler and Navier-Stokes flows," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2071-2084, November.
    2. Martin Sauer, 2016. "$$L^1$$ L 1 -Uniqueness of Kolmogorov Operators Associated with Two-Dimensional Stochastic Navier–Stokes Coriolis Equations with Space–Time White Noise," Journal of Theoretical Probability, Springer, vol. 29(2), pages 569-589, 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:31:y:1989:i:1:p:1-31. 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.