Local no-slip Navier--Stokes equations under stochastic parabolicity

We consider the three-dimensional incompressible Navier--Stokes equation on a bounded smooth domain with no-slip boundary condition and finitely many smooth, divergence-free, boundary-tangent transport noises. We prove local pathwise well-posedness under the stochastic parabolicity condition $\nu I-\frac12\sum_k b_k\otimes b_k\geq\delta I>0$, without an additional smallness assumption on the noise. For smooth compatible initial data the solution is continuous in $B^{1/2}_{4,4}$ and belongs locally to $L^4$ in time with values in $W^{1,4}_0$. Uniqueness holds in this entire path class, and the solutions depend continuously in probability on the initial data after common stopping. The proof first controls constant transport on periodic channels and full interior tori. Localization through the Stokes energy form preserves the weak Dirichlet scale; a quantitative square-root comparison makes its errors small enough to recover the physical-domain estimate.