Operator differential-algebraic equations with noise arising in fluid dynamics
The authors study linear stochastic operator differential algebraic equations (DAEs) that arise in fluid dynamics, notably the Stokes equation as a prototype. Deterministic regularization techniques are combined with polynomial chaos expansion methods to obtain explicit solutions. Existence and uniqueness of the solutions is proven in Kondratiev spaces of stochastic processes. The stochastic operator theoretical background of the paper relies on [\textit{T. Levajković} et al., Electron. J. Probab. 20, Paper No. 19, 23 p. (2015; Zbl 1321.60137)].
scientific article; zbMATH DE number 6704116
scientific article