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Coupling the Stokes and Navier-Stokes equations with two scalar nonlinear parabolic equations

 

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Opened Access Coupling the Stokes and Navier-Stokes equations with two scalar nonlinear parabolic equations
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Author: Gómez Mármol, María Macarena
Ortegón Gallego, Francisco
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 1999
Published in: Mathematical Modelling and Numerical Analysis, 33 (1), 157-167.
Document type: Article
Abstract: This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the N components of the velocity field u coupled with two scalar quantities θ and ϕ. The system presents nonlinear turbulent viscosity A(θ, ϕ) and nonlinear source terms of the form θ2|∇u| 2 and θϕ|∇u| 2 lying in L1. Some existence results are shown in this paper, including L∞-estimates and positivity for both θ and ϕ. Nous étudions un système non-linéaire d’équations du type parabolique provenant de la modélisation de la turbulence. Les inconnues sont les N composantes du champ des vitesses u couplées avec deux grandeurs scalaires θ et ϕ. Ce système présente un terme de diffusion non-linéaire sous forme matricielle A(θ,ϕ) et les termes sources non-linéaires θ2|∇u| 2 et θϕ|∇u| 2 appartenant à L1. On démontre alors quelques résultats d’existence de solutions, ainsi que des estimations dans L∞ et positivité pour θ et ϕ.
Cite: Gómez Mármol, M.M. y Ortegón Gallego, F. (1999). Coupling the Stokes and Navier-Stokes equations with two scalar nonlinear parabolic equations. Mathematical Modelling and Numerical Analysis, 33 (1), 157-167.
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URI: http://hdl.handle.net/11441/42067

DOI: 10.1051/m2an:1999110

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