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We prove probabilistic well-posedness for a 2D viscous nonlinear waveequation 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 itis known that the deterministic problem is ill-posed. We show that randomperturbations of such data give rise almost surely to the existence of a uniquesolution. More specifically, we prove almost sure global well-posedness for aviscous nonlinear wave equation with the subcritical initial data in theSobolev space $\mathcal{H}^s (\mathbb{R}^2)$, $s > - \frac 15$, which arerandomly 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 perturbationsof such data (due to e.g., randomness in real-life data, numericaldiscretization, etc.) will almost surely provide a unique solution whichdepends continuously on the data in the $\mathcal{H}^s$ topology.

Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid-structure interaction