Geodesic
Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations
Bessaih, Hakima1  ; Trabelsi, Saber2 ; Zorgati, Hamdi3
1 University of Wyoming, Department of Mathematics, Dept. 3036, 1000 East University Avenue, Laramie WY 82071, US.
2 Division of Mathematical and Computer Science and Engineering, King Abdullah University of Science and Technology, 23955-6900 Thuwal, Saudi Arabia.
3 Département de Mathématiques, Campus Universitaire, Université Tunis El Manar 2092, Tunisia.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1817-1823

Voir la notice de l'article provenant de la source Numdam

We study a modified three-dimensional incompressible anisotropic Navier−Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one. This modification appears naturally in porous media when a fluid obeys the Darcy−Forchheimer law instead of the classical Darcy law. We prove global in time existence and uniqueness of solutions without assuming the smallness condition on the initial data. This improves the result obtained for the classical 3D incompressible anisotropic Navier−Stokes equations.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016008
Classification : 35Q30, 35Q35, 76D05, 76D03, 76S05
Keywords: Navier−Stokes equations, Brinkman−Forchheimer-extended Darcy model, anisotropic viscosity

Bessaih, Hakima 1 ; Trabelsi, Saber 2 ; Zorgati, Hamdi 3

1 University of Wyoming, Department of Mathematics, Dept. 3036, 1000 East University Avenue, Laramie WY 82071, US.
2 Division of Mathematical and Computer Science and Engineering, King Abdullah University of Science and Technology, 23955-6900 Thuwal, Saudi Arabia.
3 Département de Mathématiques, Campus Universitaire, Université Tunis El Manar 2092, Tunisia. 
@article{M2AN_2016__50_6_1817_0,
     author = {Bessaih, Hakima and Trabelsi, Saber and Zorgati, Hamdi},
     title = {Existence and uniqueness of global solutions for the modified anisotropic {3D} {Navier\ensuremath{-}Stokes} equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1817--1823},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {6},
     year = {2016},
     doi = {10.1051/m2an/2016008},
     zbl = {1356.35155},
     mrnumber = {3580123},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2016008/}
}
TY  - JOUR
AU  - Bessaih, Hakima
AU  - Trabelsi, Saber
AU  - Zorgati, Hamdi
TI  - Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2016
SP  - 1817
EP  - 1823
VL  - 50
IS  - 6
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2016008/
DO  - 10.1051/m2an/2016008
LA  - en
ID  - M2AN_2016__50_6_1817_0
ER  - 
%0 Journal Article
%A Bessaih, Hakima
%A Trabelsi, Saber
%A Zorgati, Hamdi
%T Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2016
%P 1817-1823
%V 50
%N 6
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2016008/
%R 10.1051/m2an/2016008
%G en
%F M2AN_2016__50_6_1817_0
Bessaih, Hakima; Trabelsi, Saber; Zorgati, Hamdi. Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1817-1823. doi: 10.1051/m2an/2016008

Cité par Sources :