APDE seminar@BCAM: Global strong well-posedness for a stochastic fluid-structure interaction problem

Abstract

Fluid-structure interaction (FSI) problems arise in many real-world applications, such as blood flow in arteries. Both the fluid dynamics of the blood and the mechanical response of the vessel wall may be influenced by random effects. Well-posedness results for stochastic FSI problems therefore provide mathematical support for the robustness of such models under stochastic perturbations.

In this talk, we discuss global strong pathwise well-posedness for a stochastic FSI problem coupling a 2D incompressible Navier-Stokes fluid to a 1D Kirchhoff plate with Kelvin-Voigt-type damping. The stochastic forcing is modeled by a cylindrical Wiener process and acts on both the fluid equation and the structure equation. We first adapt an approach due to Da Prato and Zabczyk to split the problem into a linear stochastic problem and a nonlinear deterministic remainder. For the linear stochastic problem, we use the theory of stochastic maximal regularity. To this end, we show that the underlying fluid-structure operator admits a bounded H∞-calculus. Quasilinear evolution theory then yields local-in-time well-posedness and a blow-up criterion for the deterministic remainder. Finally, we derive energy and higher-order a priori estimates to rule out the blow-up scenario and obtain global-in-time existence. This talk is based on joint work with M. Hieber and A. Roy.