Large deviations for the Boussinesq equations under random influences

By Jinqiao Duan, Annie Millet. 2008

149 citations recorded by the source corpus.

A Boussinesq model for the Benard 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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/7fa9004e828ad5875d2a1e266e903d009cbe3792

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Zdzisław Brzeźniak
2. Elżbieta Motyl
3. Igor D. Chueshov
4. Paul Dupuis
5. A. Budhiraja
6. Annie Millet

In Computational Theory and Mathematics

1. Zdzisław Brzeźniak
2. Igor D. Chueshov
3. Elżbieta Motyl
4. Markus Fischer
5. Paul Dupuis
6. A. Budhiraja
7. Annie Millet
8. Bixiang Wang

In Finance

1. A. Budhiraja
2. Paul Dupuis
3. Zdzisław Brzeźniak
4. Igor D. Chueshov
5. Elżbieta Motyl
6. Markus Fischer
7. Annie Millet
8. Tusheng Zhang

Citations in the corpus

• Large deviation properties of weakly interacting processes via weak convergence methods (2010, background): “Finally, we remark that variational representations for Brownian motions and Poisson random measures [3, 4, 5] have proved to be useful for the study of small noise large deviation problems and many recent papers have applied these results to a variety of in nite dimensional small noise systems [10,”
• Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise (2008, unknown): “Keywords: Stochastic evolution equation, large deviation principle, Laplace principle, variational approach, weak convergence approach, reaction-diffusion equations, porous media equations, fast diffusion equations, p-Laplace equation.”
• The existence of martingale solutions to the stochastic Boussinesq equations (2011, methodology): “[8] J. Duan, A. Millet, “Large deviations for the Boussinesq equations under random influences”, Stochastic processes and their Applications, Vol. 119, No. 6, pp. 2052-2081, 2009.”
• Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations (2008, methodology): “5 and easier; it will be sketched (see also [13], Proposition 4.”