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nonlinear parabolic systems

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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1 results

Coupling the Stokes and Navier–Stokes equations with two scalarnonlinear parabolic equations
Macarena Gómez Mármol, Francisco Ortegón Gallego
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 33 / Issue 1 / January 1999

Published online by Cambridge University Press:

15 August 2002, pp. 157-167

Print publication:

January 1999
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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.