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2022-07-01Zeitschriftenartikel DOI: 10.18452/25417
On the existence of global‐in‐time weak solutions and scaling laws for Kolmogorov's two‐equation model for turbulence
dc.contributor.authorMielke, Alexander
dc.contributor.authorNaumann, Joachim
dc.date.accessioned2022-10-27T13:43:01Z
dc.date.available2022-10-27T13:43:01Z
dc.date.issued2022-07-01none
dc.date.updated2022-09-21T22:28:10Z
dc.identifier.urihttp://edoc.hu-berlin.de/18452/26108
dc.description.abstractThis paper is concerned with Kolmogorov's two-equation model for turbulence in R 3 $\mathbb {R}^3$ involving the mean velocity u, the pressure p, an average frequency ω > 0 $\omega >0$ , and a mean turbulent kinetic energy k. We consider the system with space-periodic boundary conditions in a cube Ω = ( ] 0 , a [ ) 3 $\Omega =({]0,a[}){}^3$ , which is a good choice for studying the decay of free turbulent motion sufficiently far away from boundaries. In particular, this choice is compatible with the rich set of similarity transformations for turbulence. The main part of this work consists in proving existence of global weak solutions of this model. For this we approximate the system by adding a suitable regularizing r-Laplacian and invoke existence result for evolutionary equations with pseudo-monotone operators. An important point constitutes the derivation of pointwise a priori estimates for ω (upper and lower) and k (only lower) that are independent of the box size a, thus allow us to control the parabolicity of the diffusion operators.eng
dc.description.sponsorshipDeutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659
dc.language.isoengnone
dc.publisherHumboldt-Universität zu Berlin
dc.rights(CC BY-NC-ND 4.0) Attribution-NonCommercial-NoDerivatives 4.0 Internationalger
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510 Mathematiknone
dc.titleOn the existence of global‐in‐time weak solutions and scaling laws for Kolmogorov's two‐equation model for turbulencenone
dc.typearticle
dc.identifier.urnurn:nbn:de:kobv:11-110-18452/26108-5
dc.identifier.doihttp://dx.doi.org/10.18452/25417
dc.type.versionpublishedVersionnone
local.edoc.pages31none
local.edoc.type-nameZeitschriftenartikel
local.edoc.container-typeperiodical
local.edoc.container-type-nameZeitschrift
dc.description.versionPeer Reviewednone
dc.identifier.eissn1521-4001
dcterms.bibliographicCitation.doi10.1002/zamm.202000019none
dcterms.bibliographicCitation.journaltitleZAMM : journal of applied mathematics and mechanics = Zeitschrift für angewandte Mathematik und Mechaniknone
dcterms.bibliographicCitation.volume102none
dcterms.bibliographicCitation.issue9none
dcterms.bibliographicCitation.articlenumbere202000019none
dcterms.bibliographicCitation.originalpublishernameWiley-VCHnone
dcterms.bibliographicCitation.originalpublisherplaceBerlinnone
bua.departmentMathematisch-Naturwissenschaftliche Fakultätnone

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