IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v179y2025ics0304414924002114.html
   My bibliography  Save this article

Well-Posedness of the generalised Dean–Kawasaki Equation with correlated noise on bounded domains

Author

Listed:
  • Popat, Shyam

Abstract

In this paper, we extend the notion of stochastic kinetic solutions introduced in Fehrman and Gess (2024) to establish the well-posedness of stochastic kinetic solutions of generalised Dean–Kawasaki equations with correlated noise on bounded, C2-domains with Dirichlet boundary conditions. The results apply to a wide class of non-negative boundary data, which is based on certain a priori estimates for the solutions, that encompasses all non-negative constant functions including zero and all smooth functions bounded away from zero.

Suggested Citation

  • Popat, Shyam, 2025. "Well-Posedness of the generalised Dean–Kawasaki Equation with correlated noise on bounded domains," Stochastic Processes and their Applications, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:spapps:v:179:y:2025:i:c:s0304414924002114
    DOI: 10.1016/j.spa.2024.104503
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924002114
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104503?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. Clini, Andrea, 2023. "Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 428-498.
    2. Kawasaki, Kyozi, 1994. "Stochastic model of slow dynamics in supercooled liquids and dense colloidal suspensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(1), pages 35-64.
    3. Gess, Benjamin & Souganidis, Panagiotis E., 2017. "Stochastic non-isotropic degenerate parabolic–hyperbolic equations," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2961-3004.
    Full references (including those not matched with items on IDEAS)

    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. Mykhaylo Shkolnikov & Lane Chun Yeung, 2024. "From rank-based models with common noise to pathwise entropy solutions of SPDEs," Papers 2406.07286, arXiv.org.
    2. Vitalii Konarovskyi & Victor Marx, 2023. "On Conditioning Brownian Particles to Coalesce," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2126-2164, December.
    3. Kolli, Praveen & Sarantsev, Andrey, 2019. "Large rank-based models with common noise," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 29-35.
    4. Saeed, Mahdisoltani & Ramin, Golestanian, 2023. "Nonequilibrium phenomena in driven and active Coulomb field theories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 631(C).

    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:179:y:2025:i:c:s0304414924002114. 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.