  We consider a stochastic 2D Navier-Stokes equation in a bounded domain. The
random force is assumed to be non-degenerate and periodic in time, its law has
a support localised with respect to both time and space. Slightly strengthening
the conditions in the pioneering work about exponential ergodicity by Shirikyan
[Shi15], we prove that the stochastic system satisfies Donsker-Varadhan typle
large deviations principle. Our proof is based on a criterion of [JNPS15] in
which we need to verify uniform irreducibility and uniform Feller property for
the related Feynman-Kac semigroup.
