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Large deviations for the Boussinesq equations under random influences

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

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