  We introduce an extended variational framework for nonlinear SPDEs with
unbounded noise, defining three different solution types of increasing strength
along with criteria to establish their existence. The three notions can be
understood as probabilistically and analytically weak, probabilistically strong
and analytically weak, as well as probabilistically and analytically strong.
Our framework facilitates several well-posedness results for the Navier-Stokes
Equation with transport noise, equipped with the no-slip and Navier boundary
conditions.
