Issue |
ESAIM: M2AN
Volume 33, Number 1, January Fabruary 1999
|
|
---|---|---|
Page(s) | 157 - 167 | |
DOI | https://doi.org/10.1051/m2an:1999110 | |
Published online | 15 August 2002 |
Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations
1
Departamento de Ecuaciones Diferenciales y Análisis Numérico
Universidad de Sevilla, Spain. ortegon@numer.us.es.
2
Departamento de Matemáticas, Universidad de
Cádiz, Spain. francisco.ortegon@uca.es.
Received:
3
December
1996
Revised:
18
November
1997
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 and nonlinear
source terms of the form
and
lying in L1. Some existence results are shown in this paper, including
-estimates and positivity for both θ and φ.
Résumé
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 et les termes sources non-linéaires
et
appartenant à L1. On démontre alors quelques résultats d'existence de solutions, ainsi
que des estimations dans
et positivité pour θ et φ.
Mathematics Subject Classification: 35K45 / 35K60 / 35Q35
Key words: Nonlinear parabolic systems / Stokes and Navier-Stokes equations
© EDP Sciences, SMAI, 1999
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