Operator differential-algebraic equations with noise arising in fluid dynamics

dc.contributor.authorAltmann, Robert
dc.contributor.authorLevajković, Tijana
dc.contributor.authorMena, Hermann
dc.date.accessioned2017-08-28T11:30:36Z
dc.date.available2017-08-28T11:30:36Z
dc.date.issued2016
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.eissn1436-5081
dc.identifier.issn0026-9255
dc.identifier.urihttp://depositonce.tu-berlin.de/handle/11303/6638
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-6079
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddc510 Mathematik
dc.subject.otheroperator DAEen
dc.subject.othernoise disturbancesen
dc.subject.otherchaos expansionen
dc.subject.otherItô-Skorokhod integralen
dc.subject.otherstochastic convolutionen
dc.subject.otherregularizationen
dc.titleOperator differential-algebraic equations with noise arising in fluid dynamicsen
dc.typeArticle
dc.type.versionpublishedVersion
dcterms.bibliographicCitation.doi10.1007/s00605-016-0931-z
dcterms.bibliographicCitation.issue4
dcterms.bibliographicCitation.journaltitleMonatshefte für Mathematik
dcterms.bibliographicCitation.originalpublishernameSpringer
dcterms.bibliographicCitation.originalpublisherplaceWien
dcterms.bibliographicCitation.pageend780
dcterms.bibliographicCitation.pagestart741
dcterms.bibliographicCitation.volume182
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik>FG Numerische Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Numerische Mathematikde
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlin
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