Operator Differential Algebraic Equations with Noise Arising in Fluid Dynamics

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dc.contributor.authorAltmann, Robert
dc.contributor.authorLevajković, Tijana
dc.contributor.authorMena, Hermann
dc.date.accessioned2021-12-17T10:12:58Z
dc.date.available2021-12-17T10:12:58Z
dc.date.issued2015-11-30
dc.description.abstractWe 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.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15832
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14605
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otheroperators DAEen
dc.subject.othernoise disturbancesen
dc.subject.otherchaos expansionsen
dc.subject.otherIto-Skorokhod integralen
dc.subject.otherstochastic convolutionen
dc.subject.otherregularizationen
dc.titleOperator Differential Algebraic Equations with Noise Arising in Fluid Dynamicsen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2015, 31en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200065J10 Equations with linear operatorsen
tub.subject.msc200060H40 White noise theoryen
tub.subject.msc200060H30 Applications of stochastic analysisen
tub.subject.msc200035R60 Partial differential equations with randomnessen

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