IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i6p2052-2081.html
   My bibliography  Save this article

Large deviations for the Boussinesq equations under random influences

Author

Listed:
  • Duan, Jinqiao
  • Millet, Annie

Abstract

A Boussinesq model for the Bénard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier-Stokes equations and the transport equation for temperature. Large deviations are proved, using a weak convergence approach based on a variational representation of functionals of infinite-dimensional Brownian motion.

Suggested Citation

  • Duan, Jinqiao & Millet, Annie, 2009. "Large deviations for the Boussinesq equations under random influences," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2052-2081, June.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:6:p:2052-2081
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00157-9
    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.

    References listed on IDEAS

    as
    1. Sritharan, S.S. & Sundar, P., 2006. "Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1636-1659, November.
    2. Chenal, Fabien & Millet, Annie, 1997. "Uniform large deviations for parabolic SPDEs and applications," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 161-186, December.
    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. Pappalettera, Umberto, 2022. "Large deviations for stochastic equations in Hilbert spaces with non-Lipschitz drift," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 1-20.
    2. 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.
    3. 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.
    4. Budhiraja, Amarjit & Chen, Jiang & Dupuis, Paul, 2013. "Large deviations for stochastic partial differential equations driven by a Poisson random measure," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 523-560.
    5. Du, Lihuai & Zhang, Ting, 2020. "Local and global existence of pathwise solution for the stochastic Boussinesq equations with multiplicative noises," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1545-1567.
    6. Maroulas, Vasileios & Pan, Xiaoyang & Xiong, Jie, 2020. "Large deviations for the optimal filter of nonlinear dynamical systems driven by Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 203-231.
    7. Cai, Yujie & Huang, Jianhui & Maroulas, Vasileios, 2015. "Large deviations of mean-field stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 1-9.
    8. Deugoué, G. & Tachim Medjo, T., 2023. "Large deviation for a 3D globally modified Cahn–Hilliard–Navier–Stokes model under random influences," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 33-71.
    9. Hakima Bessaih & Annie Millet, 2022. "Speed of Convergence of Time Euler Schemes for a Stochastic 2D Boussinesq Model," Mathematics, MDPI, vol. 10(22), pages 1-39, November.
    10. Ganguly, Arnab, 2018. "Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2179-2227.

    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. Swie[combining cedilla]ch, Andrzej, 2009. "A PDE approach to large deviations in Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1081-1123, April.
    2. 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.
    3. Maroulas, Vasileios & Xiong, Jie, 2013. "Large deviations for optimal filtering with fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2340-2352.
    4. Gautier, Eric, 2005. "Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1904-1927, December.
    5. Budhiraja, Amarjit & Chen, Jiang & Dupuis, Paul, 2013. "Large deviations for stochastic partial differential equations driven by a Poisson random measure," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 523-560.
    6. Deugoué, G. & Tachim Medjo, T., 2023. "Large deviation for a 3D globally modified Cahn–Hilliard–Navier–Stokes model under random influences," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 33-71.
    7. Ganguly, Arnab, 2018. "Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2179-2227.
    8. Mohan, Manil T., 2020. "Well posedness, large deviations and ergodicity of the stochastic 2D Oldroyd model of order one," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4513-4562.
    9. Ankit Kumar & Manil T. Mohan, 2023. "Large Deviation Principle for Occupation Measures of Stochastic Generalized Burgers–Huxley Equation," Journal of Theoretical Probability, Springer, vol. 36(1), pages 661-709, March.
    10. Sundar, P. & Yin, Hong, 2009. "Existence and uniqueness of solutions to the backward 2D stochastic Navier-Stokes equations," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1216-1234, April.
    11. Arturo Kohatsu & D. Márquez Carreras & M. Sanz Solé, 1999. "Asymptotic behaviour of the density in a parabolic SPDE," Economics Working Papers 371, Department of Economics and Business, Universitat Pompeu Fabra.
    12. 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.
    13. Cardon-Weber, Caroline, 1999. "Large deviations for a Burgers'-type SPDE," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 53-70, November.
    14. Cai, Yujie & Huang, Jianhui & Maroulas, Vasileios, 2015. "Large deviations of mean-field stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 1-9.
    15. Eric Gautier, 2005. "Exit from a Neighborhood of Zero for Weakly Damped Stochastic Nonlinear Schrödinger Equations," Working Papers 2005-21, Center for Research in Economics and Statistics.
    16. Wei Wang & Jianliang Zhai & Tusheng Zhang, 2022. "Stochastic Two-Dimensional Navier–Stokes Equations on Time-Dependent Domains," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2916-2939, December.
    17. A. Kohatsu-Higa & D. Márquez-Carreras & M. Sanz-Solé, 2001. "Asymptotic Behavior of the Density in a Parabolic SPDE," Journal of Theoretical Probability, Springer, vol. 14(2), pages 427-462, April.
    18. 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.
    19. Xiuwei Yin & Jiang-Lun Wu & Guangjun Shen, 2022. "Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2940-2959, December.

    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:119:y:2009:i:6:p:2052-2081. 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.