IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v128y2018i8p2710-2749.html
   My bibliography  Save this article

Optimal control for two-dimensional stochastic second grade fluids

Author

Listed:
  • Chemetov, Nikolai
  • Cipriano, Fernanda

Abstract

This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The control acts through an external stochastic force and we search for a control that minimizes a cost functional. We show that the Gâteaux derivative of the control to state map is a stochastic process being the unique solution of the stochastic linearized state equation. The well-posedness of the corresponding stochastic backward adjoint equation is also established, allowing to derive the first order optimality condition.

Suggested Citation

  • Chemetov, Nikolai & Cipriano, Fernanda, 2018. "Optimal control for two-dimensional stochastic second grade fluids," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2710-2749.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:8:p:2710-2749
    DOI: 10.1016/j.spa.2017.09.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414917302454
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2017.09.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Cipriano, Fernanda & Torrecilla, Iván, 2015. "Inviscid limit for 2D stochastic Navier–Stokes equations," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2405-2426.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Nikolai Chemetov & Fernanda Cipriano, 2024. "A Boundary Control Problem for Stochastic 2D-Navier–Stokes Equations," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1847-1879, November.
    2. Evgenii S. Baranovskii & Mikhail A. Artemov, 2021. "Optimal Control for a Nonlocal Model of Non-Newtonian Fluid Flows," Mathematics, MDPI, vol. 9(3), pages 1-16, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:128:y:2018:i:8:p:2710-2749. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.