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

We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid–structure interaction between 3D incompressible, Stokes flow and elastodynamics of stretched membrane. The focus is on (rough) data, often arising in real-life problems, which it known that the deterministic problem ill-posed. show random perturbations such data give rise almost surely to existence unique solution. More specifically, we sure global with subcritical initial Sobolev space Hs(R2), s>?15, are randomly perturbed using Wiener randomization. This result shows ‘robustness’ problems/models, provides confidence even ‘rough data’ (data Hs, s>?15) (due to, e.g. randomness numerical discretization, etc.) will provide solution depends continuously Hs topology.