  We study well-posedness for fluid-structure interaction driven by stochastic
forcing. This is of particular interest in real-life applications where forcing
and/or data have a strong stochastic component. The prototype model studied
here is a stochastic viscous wave equation, which arises in modeling the
interaction between Stokes flow and an elastic membrane. To account for
stochastic perturbations, the viscous wave equation is perturbed by spacetime
white noise scaled by a nonlinear Lipschitz function, which depends on the
solution. We prove the existence of a unique function-valued stochastic mild
solution to the corresponding Cauchy problem in spatial dimensions one and two.
Additionally, we show that up to a modification, the stochastic mild solution
is $\alpha$-H\"{o}lder continuous for almost every realization of the
solution's sample path, where $\alpha\in[0,1)$ for spatial dimension $n=1$, and
$\alpha \in [0,1/2)$ for spatial dimension $n=2$. This result contrasts the
known results for the heat and wave equations perturbed by spacetime white
noise, including the damped wave equation perturbed by spacetime white noise,
for which a function-valued mild solution exists only in spatial dimension one
and not higher. Our results show that dissipation due to fluid viscosity, which
is in the form of the Dirichlet-to-Neumann operator applied to the time
derivative of the membrane displacement, sufficiently regularizes the roughness
of white noise in the stochastic viscous wave equation to allow the stochastic
mild solution to exist even in dimension two, which is the physical dimension
of the problem. To the best of our knowledge, this is the first result on
well-posedness for a stochastically perturbed fluid-structure interaction
problem.
