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We prove the existence and uniqueness of global, probabilistically strong,analytically strong solutions of the 2D Stochastic Navier-Stokes Equation underNavier boundary conditions. The choice of noise includes a large class ofadditive, multiplicative and transport models. We emphasise that with atransport type noise, the Navier boundary conditions enable direct energyestimates which appear to be prohibited for the usual no-slip condition. Theimportance of the Stochastic Advection by Lie Transport (SALT) structure, incomparison to a purely transport Stratonovich noise, is also highlighted inthese estimates. In the particular cases of SALT noise, the free boundarycondition and a domain of non-negative curvature, the inviscid limit exists andis a global, probabilistically weak, analytically weak solution of thecorresponding Stochastic Euler Equation.

Navier-Stokes Equations with Navier Boundary Conditions and Stochastic Lie Transport: Well-Posedness and Inviscid Limit