We consider a coupled system of PDEs for two scalar functions u and k in a bounded domain ( or ) 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 ( ou ). 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.
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Joachim Naumann 1; Joerg Wolf 2
@article{CRMATH_2012__350_1-2_45_0, author = {Joachim Naumann and Joerg Wolf}, title = {Existence of weak solutions to a simplified steady system of turbulence modeling}, journal = {Comptes Rendus. Math\'ematique}, pages = {45--50}, publisher = {Elsevier}, volume = {350}, number = {1-2}, year = {2012}, doi = {10.1016/j.crma.2011.12.008}, language = {en}, }
TY - JOUR AU - Joachim Naumann AU - Joerg Wolf TI - Existence of weak solutions to a simplified steady system of turbulence modeling JO - Comptes Rendus. Mathématique PY - 2012 SP - 45 EP - 50 VL - 350 IS - 1-2 PB - Elsevier DO - 10.1016/j.crma.2011.12.008 LA - en ID - CRMATH_2012__350_1-2_45_0 ER -
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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