Strong well-posedness for a stochastic fluid-rigid body system via stochastic maximal regularity

Abstract

We develop a rigorous analytical framework for a coupled stochastic fluid-rigid body system in ${\mathbb{R}}^3$. The model describes the motion of a rigid ball immersed in an incompressible Newtonian fluid subjected to both additive noise in the fluid and body equations and transport-type noise in the fluid equation. We establish local strong well-posedness of the resulting system by combining stochastic maximal ${\mathrm{L}}^p$-regularity theory with a decoupling approach for the associated fluid-structure operator. A key step is to prove the boundedness of the ${\mathcal{H}}^{\infty }$-calculus for this operator. In addition, we provide blow-up criteria for the maximal existence time of solutions. To our knowledge, this is the first rigorous treatment of strong solutions of stochastic fluid-structure interactions.

arXiv commentAccepted for publication in the Journal of the London Mathematical Society