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 . 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 ‐regularity theory with a decoupling approach for the associated fluid–structure operator. A key step is to prove the boundedness of the ‐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.