Comptes Rendus
no. 1-2
Partial Differential Equations
Existence of weak solutions to a simplified steady system of turbulence modeling

Presented by: Philippe G. Ciarlet

Joachim Naumann1; Joerg Wolf2
1 Department of Mathematics, Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany
2 Faculty of Mathematics, University of Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
Comptes Rendus. Mathématique, Volume 350 (2012) no. 1-2, pp. 45-50.

We consider a coupled system of PDEs for two scalar functions u and k in a bounded domain Ω⊂Rd (d=2 or d=3) of Prandtlʼs (1945) turbulence model (u = “one-dimensional” mean velocity, k = turbulent mean kinetic energy). We prove the existence of weak solutions to the system under consideration with homogeneous Dirichlet conditions on u, and mixed boundary conditions on k.

On considère un système couplé dʼéquations aux dérivées partielles pour des fonctions scalaires u et k dans un domaine borné de Rd (d=2 ou d=3). Ce système représente une version simplifiée du modèle stationaire de turbulence de Prandtl (1945) (u = vitesse « unidimensionnelle » moyenne, k = énergie cinétique turbulente moyenne). On établit lʼexistence des solutions faibles du système envisagé avec des conditions aux limites homogènes de Dirichlet pour u, et des conditions aux limites mixtes homogènes de Neumann pour k.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.12.008

Joachim Naumann 1; Joerg Wolf 2

1 Department of Mathematics, Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany
2 Faculty of Mathematics, University of Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany 
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Joachim Naumann; Joerg Wolf. Existence of weak solutions to a simplified steady system of turbulence modeling. Comptes Rendus. Mathématique, Volume 350 (2012) no. 1-2, pp. 45-50. doi : 10.1016/j.crma.2011.12.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.12.008/

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