# Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations

Macarena Gómez Mármol; Francisco Ortegón Gallego

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 1, page 157-167
- ISSN: 0764-583X

## Access Full Article

top## Abstract

top## How to cite

topGómez Mármol, Macarena, and Ortegón Gallego, Francisco. "Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations." ESAIM: Mathematical Modelling and Numerical Analysis 33.1 (2010): 157-167. <http://eudml.org/doc/197545>.

@article{GómezMármol2010,

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 $A(\theta,\varphi)$ and nonlinear
source terms of the form $\theta^2|\nabla u|^2$ and $\theta\varphi|\nabla u|^2$
lying in L1. Some existence results are shown in this paper, including
$L^\infty$-estimates and positivity for both θ and φ.
},

author = {Gómez Mármol, Macarena, Ortegón Gallego, Francisco},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Nonlinear parabolic systems; Stokes and Navier-Stokes
equations; nonlinear turbulent viscosity; nonlinear source terms; existence; positivity},

language = {eng},

month = {3},

number = {1},

pages = {157-167},

publisher = {EDP Sciences},

title = {Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations},

url = {http://eudml.org/doc/197545},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Gómez Mármol, Macarena

AU - Ortegón Gallego, Francisco

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 1

SP - 157

EP - 167

AB -
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 $A(\theta,\varphi)$ and nonlinear
source terms of the form $\theta^2|\nabla u|^2$ and $\theta\varphi|\nabla u|^2$
lying in L1. Some existence results are shown in this paper, including
$L^\infty$-estimates and positivity for both θ and φ.

LA - eng

KW - Nonlinear parabolic systems; Stokes and Navier-Stokes
equations; nonlinear turbulent viscosity; nonlinear source terms; existence; positivity

UR - http://eudml.org/doc/197545

ER -

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.