Basma Jaffal-Mourtada Global existence of the 3D rotating second grade fluid system Article de journal Asymptotic Analysis, p. 1-32, 2020. Résumé | Liens | BibTeX @article{Jaffal-Mourtada2020,
title = {Global existence of the 3D rotating second grade fluid system},
author = {Basma Jaffal-Mourtada},
doi = {10.3233/ASY-201644},
year = {2020},
date = {2020-11-02},
journal = {Asymptotic Analysis},
pages = {1-32},
abstract = {We consider the equations of a rotating incompressible non-Newtonian fluid flow of grade two in a three dimensional torus. We prove two different results of global existence of strong solutions. In the first case, we consider that the elasticity coefficient α is arbitrary and we suppose that the third components of the vertical average of the initial data and of the forcing term are small compared to the horizontal components. In the second case, we consider a forcing term and initial data of arbitrary size but we restrict the size of α. In both cases, we show that the limit system is composed of a linear system and a second grade fluid system with two variables and three components. },
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We consider the equations of a rotating incompressible non-Newtonian fluid flow of grade two in a three dimensional torus. We prove two different results of global existence of strong solutions. In the first case, we consider that the elasticity coefficient α is arbitrary and we suppose that the third components of the vertical average of the initial data and of the forcing term are small compared to the horizontal components. In the second case, we consider a forcing term and initial data of arbitrary size but we restrict the size of α. In both cases, we show that the limit system is composed of a linear system and a second grade fluid system with two variables and three components. |
Kamel Hamdache; Basma Jaffal-Mourtada Existence and uniqueness of solutions for the magnetohydrodynamic flow of a second grade fluid Article de journal Math. Meth. Appl. Sci., 36 (4), p. 478-496, 2012. Résumé | Liens | BibTeX @article{Jaffal-Mourtada2012,
title = {Existence and uniqueness of solutions for the magnetohydrodynamic flow of a second grade fluid},
author = {Kamel Hamdache and Basma Jaffal-Mourtada },
doi = {10.1002/mma.2608},
year = {2012},
date = {2012-06-21},
journal = {Math. Meth. Appl. Sci.},
volume = {36},
number = {4},
pages = {478-496},
abstract = {In this work, we consider the flow of a second grade fluid in a conducting domain of R3 and in the presence of a magnetic field. When the initial data are of arbitrary size, we prove that the solution of the magnetohydrodynamics problem exists for a small time and is unique. We also show the global existence of solutions for small initial data. },
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this work, we consider the flow of a second grade fluid in a conducting domain of R3 and in the presence of a magnetic field. When the initial data are of arbitrary size, we prove that the solution of the magnetohydrodynamics problem exists for a small time and is unique. We also show the global existence of solutions for small initial data. |
Basma Jaffal-Mourtada Long-time asymptotics of the second grade fluid equations on R^2 Article de journal Dynamics of Partial Differential Equations, 8 (3), p. 185-223, 2011. Résumé | Liens | BibTeX @article{Jaffal-Mourtada2011,
title = {Long-time asymptotics of the second grade fluid equations on R^2},
author = {Basma Jaffal-Mourtada },
doi = {10.4310/DPDE.2011.v8.n3.a2},
year = {2011},
date = {2011-09-15},
journal = {Dynamics of Partial Differential Equations},
volume = {8},
number = {3},
pages = {185-223},
abstract = {We study the large time behavior of solutions of the second grade fluid system in the space R^2 . Using scaled variables and introducing several functionals in weighted Sobolev spaces, we prove that the solution of the second grade fluid equations converges to the Oseen vortex, if the initial data are small enough. We also give an estimate of the rate of convergence.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We study the large time behavior of solutions of the second grade fluid system in the space R^2 . Using scaled variables and introducing several functionals in weighted Sobolev spaces, we prove that the solution of the second grade fluid equations converges to the Oseen vortex, if the initial data are small enough. We also give an estimate of the rate of convergence. |
