  In this article, we establish the \textsl{Wong-Zakai approximation} result
for a class of stochastic partial differential equations (SPDEs) with fully
local monotone coefficients perturbed by a multiplicative Wiener noise. This
class of SPDEs encompasses various fluid dynamic models and also includes
quasi-linear SPDEs, the convection-diffusion equation, the Cahn-Hilliard
equation, and the two-dimensional liquid crystal model. It has been established
that the class of SPDEs in question is well-posed, however, the existence of a
unique solution to the associated approximating system cannot be inferred from
the solvability of the original system. We employ a Faedo-Galerkin
approximation method, compactness arguments, and Prokhorov's and Skorokhod's
representation theorems to ensure the existence of a \textsl{probabilistically
weak solution} for the approximating system. Furthermore, we also demonstrate
that the solution is pathwise unique. Moreover, the classical Yamada-Watanabe
theorem allows us to conclude the existence of a \textsl{probabilistically
strong solution} (analytically weak solution) for the approximating system.
Subsequently, we establish the Wong-Zakai approximation result for a class of
SPDEs with fully local monotone coefficients. We utilize the Wong-Zakai
approximation to establish the topological support of the distribution of
solutions to the SPDEs with fully local monotone coefficients. Finally, we
explore the physically relevant stochastic fluid dynamics models that are
covered by this work's functional framework.
