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Wentzell–Freidlin Large Deviation Principle for Stochastic Convective Brinkman–Forchheimer Equations

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Abstract

This work addresses some asymptotic behavior of solutions to stochastic convective Brinkman–Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in two and three dimensional bounded domains. Using a weak convergence approach of Budhiraja and Dupuis, we establish the Laplace principle for the strong solution to SCBF equations in a suitable Polish space. Then, the Wentzell–Freidlin type large deviation principle is derived using the well known results of Varadhan and Bryc. The large deviations for short time are also considered in this work. Furthermore, we study the exponential estimates on certain exit times associated with the solution trajectory of SCBF equations. Using contraction principle, we study these exponential estimates of exit times from the frame of reference of Wentzell–Freidlin type large deviations principle (LDP). This work also improves several LDP results available in the literature for tamed Navier–Stokes equations as well as Navier–Stokes equations with damping in bounded domains.

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Acknowledgements

M. T. Mohan would like to thank the Department of Science and Technology (DST), India for Innovation in Science Pursuit for Inspired Research (INSPIRE) Faculty Award (IFA17-MA110).

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Mohan, M.T. Wentzell–Freidlin Large Deviation Principle for Stochastic Convective Brinkman–Forchheimer Equations. J. Math. Fluid Mech. 23, 62 (2021). https://doi.org/10.1007/s00021-021-00587-x

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