Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14605
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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: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15832
http://dx.doi.org/10.14279/depositonce-14605
License: http://rightsstatements.org/vocab/InC/1.0/
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.
Subject(s): operators DAE
noise disturbances
chaos expansions
Ito-Skorokhod integral
stochastic convolution
regularization
Issue Date: 30-Nov-2015
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65J10 Equations with linear operators
60H40 White noise theory
60H30 Applications of stochastic analysis
35R60 Partial differential equations with randomness
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2015, 31
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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