Abstract
The aim of this paper is to study the local in time well possessedness of the incompressible \(k\)-\(\omega \) turbulence model in the whole 3-D space.
Similar content being viewed by others
Notes
By strong we mean a classical \(\mathcal{C}^{1}_{t}(C_{x}^{2})\) solution.
References
Cousteix, J.: Turbulence et Couche limite. Cepadues, Toulouse (Septembre 1989)
Baldwin, B.S., Barth, T.J.: A one-equation turbulence transport model for high Reynolds number wall-bounded flows. National Aeronautics and Space Administration, Ames Research Center (1990)
Spalart, P.R., Allmaras, S.R.: A one-equation turbulence model for aerodynamic flows (1992)
Wilcox, D.C.: Turbulence Modeling for CFD. DCW Industries, La Cañada Flintridge (1994)
Wilcox, D.C.: A two-equation turbulence model for wall-bounded and free-shear flows. In: 1993 AIAA 24 th Fluid Dynamics Conference (1993)
Wilcox, D.C.: Formulation of the kw turbulence model revisited. AIAA J. 46(11), 2823–2838 (2008)
Menter, F.R.: Improved two-equation \(k\)-\(\omega\) turbulence models for aerodynamic flows. NASA STI/Recon Technical Report N, 93:22809 (October 1992)
Lions, P.-L.: Mathematical Topics in Fluid Mechanics. Incompressible Models, vol. 1. Clarendon, Oxford (1996)
Lewandovski, R.: Modèles de turbulence et équations paraboliques. C. R. Math. Acad. Sci. 3(1), 835–840 (1993)
Lewandovski, R., Mohammadi, B.: Existence and positivity results for the \(\phi \)-\(\theta \) and a modified \(k\)-\(\varepsilon \) two-equation turbulence models. Math. Models Methods Appl. Sci. 3(2), 195–215 (1993)
Garcia Vasquez, C., Ortegon Gallego, F.: Sur un problème elliptique non linéaire avec diffusion singulière et second membre dans l1. C. R. Acad. Sci. 332, 145–150 (2001)
Lederer, J., Lewandovski, R.: Arans 3D model with unbounded eddy viscosities. Ann. Inst. Henri Poincaré 24, 413–441 (2007)
Julien, M.: A study of gas-particles systems. PhD thesis, École normale supérieure de Cachan-ENS Cachan (2006)
Julien, M., et al.: Local smooth solutions of the incompressible k-\(\varepsilon \) model and the low turbulent diffusion limit. Commun. Math. Sci. 6(2), 361–383 (2008)
Brezis, H.: Analyse Fonctionnelle. Masson, Paris (1983)
Taylor, M.: Partial Differential Equations, Basic Theory. Springer, New York (1996)
Constantin, P., Foias, C.: Navier Stokes Equations. University of Chicago Press, Chicago (1988)
Temam, T.: Navier-Stokes Equation. Elsevier, Amsterdam (1984)
Taylor, M.: Partial Differential Equations III, Nonlinear Equations. Springer, New York (1996)
Majda, A.: Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Springer, New York (1984)
Serre, D.: Systèmes de lois de conservations I. Diderot, Paris (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mathiaud, J., Roynard, X. Local Smooth Solutions of the Incompressible \(k\mbox{-}\omega \) Model. Acta Appl Math 146, 1–16 (2016). https://doi.org/10.1007/s10440-016-0054-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10440-016-0054-5