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Main Title: Operator differential-algebraic equations with noise arising in fluid dynamics
Author(s): Altmann, Robert
Levajković, Tijana
Mena, Hermann
Type: Article
Language Code: en
Abstract: We study linear semi-explicit stochastic operator differential algebraic equations (DAEs) for which the constraint equation is given in an explicit form. In particular, this includes the Stokes equations arising in fluid dynamics. We combine a white noise polynomial chaos expansion approach to include stochastic perturbations with deterministic regularization techniques. With this, we are able to include Gaussian noise and stochastic convolution terms as perturbations in the differential as well as in the constraint equation. By the application of the polynomial chaos expansion method, we reduce the stochastic operator DAE to an infinite system of deterministic operator DAEs for the stochastic coefficients. Since the obtained system is very sensitive to perturbations in the constraint equation, we analyze a regularized version of the system. This then allows to prove the existence and uniqueness of the solution of the initial stochastic operator DAE in a certain weighted space of stochastic processes.
Issue Date: 2016
Date Available: 28-Aug-2017
DDC Class: 510 Mathematik
Subject(s): operator DAE
noise disturbances
chaos expansion
Itô-Skorokhod integral
stochastic convolution
Journal Title: Monatshefte für Mathematik
Publisher: Springer
Publisher Place: Wien
Volume: 182
Issue: 4
Publisher DOI: 10.1007/s00605-016-0931-z
Page Start: 741
Page End: 780
EISSN: 1436-5081
ISSN: 0026-9255
Appears in Collections:FG Numerische Mathematik » Publications

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