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Coupling the Stokes and Navier–Stokes equations with two scalarnonlinear parabolic equations

Published online by Cambridge University Press:  15 August 2002

Macarena Gómez Mármol  and
Francisco Ortegón Gallego
Macarena Gómez Mármol
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico Universidad de Sevilla, Spain. [email protected].
Francisco Ortegón Gallego
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, Spain. [email protected].
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Abstract

This work deals with a system of nonlinear parabolic equations arisingin turbulence modelling. The unknowns are the N components of the velocityfield u coupled with two scalar quantities θ and φ. The systempresents nonlinear turbulent viscosity $A(\theta,\varphi)$ and nonlinearsource terms of the form $\theta^2|\nabla u|^2$ and $\theta\varphi|\nabla u|^2$ lying in L 1. Some existence results are shown in this paper, including $L^\infty$ -estimates and positivity for both θ and φ.

Keywords

Nonlinear parabolic systemsStokes and Navier-Stokesequations
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 1 , January 1999 , pp. 157 - 167
Copyright
© EDP Sciences, SMAI, 1999

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