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Title: Global-in-time existence of weak solutions to Kolmogorov's two-equation model of turbulence
Authors: Mielke, AlexanderNaumann, Joachim
Issue Date: 2015
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2078, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We consider Kolmogorov's model for the turbulent motion of an incompressible fluid in 3. This model consists in a Navier-Stokes type system for the mean flow u and two further partial differential equations: an equation for the frequency and for the kinetic energy k each. We investigate this system of partial differential equations in a cylinder x ]0,T[ ( 3 cube, 0 < T < +∞) under spatial periodic boundary conditions on x ]0,T[ and initial conditions in x {0}. We present an existence result for a weak solution {u, , k} to the problem under consideration, with , k obeying the inequalities formula1 and formula2.
Keywords: Navier-Stokes equation; Kolmogorov's turbulence model; turbulent kinetic energy; global existence for weak solutions; defect measure; scaling laws; maximum principle
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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