Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14540
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Main Title: Analysis of operator differential-algebraic equations arising in fluid dynamics. Part II. The infinite dimensional case
Author(s): Emmrich, Etienne
Mehrmann, Volker
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15767
http://dx.doi.org/10.14279/depositonce-14540
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: Existence and uniqueness of generalized solutions to initial value problems for a class of abstract differential-algebraic equations (DAEs) is shown. The class of equations covers, in particular, the Stokes and Oseen problem describing the motion of an incompressible or nearly incompressible Newtonian fluid but also their spatial semi-discretization. The equations are governed by a block operator matrix with entries that fulfill suitable inf-sup conditions. The problem data are required to satisfy appropriate consistency conditions. The results in infinite dimensions are compared in detail with those known for the DAEs that arise after semi-discretization in space. Explicit solution formulas are derived in both cases.
Subject(s): differential-algebraic equation
strangeness-index
existence
uniqueness
consistency
Duhamel's principle
Stokes equation
Oseen equation
Issue Date: 2-Sep-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 34A09 Implicit equations, differential-algebraic equations
34G10 Linear equations
76D07 Stokes and related (Oseen, etc.) flows
34H05 Control problems
65M99 None of the above, but in this section
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 28
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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