IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v124y2014i5p1974-2002.html
   My bibliography  Save this article

Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise

Author

Listed:
  • Röckner, Michael
  • Zhu, Rongchan
  • Zhu, Xiangchan

Abstract

In this paper we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear multiplicative noise provides a regularizing effect: the solutions will not blow up with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large. As applications our main results are applied to various types of SPDE such as stochastic reaction–diffusion equations, stochastic fractional Burgers equation, stochastic fractional Navier–Stokes equation, stochastic quasi-geostrophic equations and stochastic surface growth PDE.

Suggested Citation

  • Röckner, Michael & Zhu, Rongchan & Zhu, Xiangchan, 2014. "Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1974-2002.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:5:p:1974-2002
    DOI: 10.1016/j.spa.2014.01.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914000271
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2014.01.010?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. Liu, Wei & Röckner, Michael & Zhu, Xiang-Chan, 2013. "Large deviation principles for the stochastic quasi-geostrophic equations," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3299-3327.
    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. Lü, Huaxiang & Zhu, Xiangchan, 2023. "Global-in-time probabilistically strong solutions to stochastic power-law equations: Existence and non-uniqueness," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 62-98.
    2. Li, Jingna & Liu, Hongxia & Tang, Hao, 2021. "Stochastic MHD equations with fractional kinematic dissipation and partial magnetic diffusion in R2," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 139-182.
    3. Xu, Liping & Li, Zhi, 2018. "Stochastic fractional evolution equations with fractional brownian motion and infinite delay," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 36-46.
    4. Yanmei Liu & Monzorul Khan & Yubin Yan, 2016. "Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations," Mathematics, MDPI, vol. 4(3), pages 1-28, July.

    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.
    1. Salins, M., 2021. "Systems of small-noise stochastic reaction–diffusion equations satisfy a large deviations principle that is uniform over all initial data," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 159-194.

    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:124:y:2014:i:5:p:1974-2002. 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.