Large deviation principle for the three dimensional planetary geostrophic equations of large-scale ocean circulation with small multiplicative noise
Abstract
We demonstrate the large deviation principle in the small noise limit for the three dimensional stochastic planetary geostrophic equations of large-scale ocean circulation. In this paper, we first prove the well-posedness of weak solutions to this system by the method of monotonicity. As we know, a recently developed method, weak convergent method, has been employed in studying the large deviations and this method is essentially based on the main result of \cite{ba2} which discloses the variational representation of exponential integrals with respect to the Brownian noise. The It\^{o} inequality and Burkholder-Davis-Gundy inequality are the main tools in our proofs, and the weak convergence method introduced by Budhiraja, Dupuis and Ganguly in \cite{ba3} is also used to establish the large deviation principle.
Keywords
Cite
@article{arxiv.2008.02971,
title = {Large deviation principle for the three dimensional planetary geostrophic equations of large-scale ocean circulation with small multiplicative noise},
author = {Bo You},
journal= {arXiv preprint arXiv:2008.02971},
year = {2020}
}