Uniform large deviations for stochastic 2D primitive equations driven by multiplicative noise

In this paper, we establish a Freidlin–Wentzell-type large deviation principle uniformly with respect to initial conditions in bounded subsets, which do not necessarily belong to compact sets, of an infinite-dimensional Banach space for two-dimensional primitive equations driven by multiplicative noise when the noise converges to zero. The proof is based on the weak convergence approach obtained by [M. Salins, A. Budhiraja and P. Dupuis, Uniform large deviation principles for Banach space valued stochastic evolution equations, Trans. Am. Math. Soc. 372(12) (2019) 8363–8421.] and anisotropic estimates.