  We prove probabilistic well-posedness for a 2D viscous nonlinear wave
equation modeling fluid-structure interaction between a 3D incompressible,
viscous Stokes flow and nonlinear elastodynamics of a 2D stretched membrane.
The focus is on (rough) data, often arising in real-life problems, for which it
is known that the deterministic problem is ill-posed. We show that random
perturbations of such data give rise almost surely to the existence of a unique
solution. More specifically, we prove almost sure global well-posedness for a
viscous nonlinear wave equation with the subcritical initial data in the
Sobolev space $\mathcal{H}^s (\mathbb{R}^2)$, $s > - \frac 15$, which are
randomly perturbed using Wiener randomization. This result shows "robustness"
of nonlinear FSI problems/models, and provides confidence that even for the
"rough data" (data in $\mathcal{H}^s$, $s > -\frac 1 5$) random perturbations
of such data (due to e.g., randomness in real-life data, numerical
discretization, etc.) will almost surely provide a unique solution which
depends continuously on the data in the $\mathcal{H}^s$ topology.
