Bilal Al taki

Bilal Al taki
Sorbonne Université | UPMC · Laboratoire Jacques-Louis Lions (LJLL)

PhD

About

11
Publications
831
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5
Citations
Citations since 2016
11 Research Items
5 Citations
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201620172018201920202021202201234

Publications

Publications (11)
Preprint
Full-text available
The purpose of this paper is to deal with the issue of well-posedness for a class of non-Newtonian fluid dynamics equations. These sets of equations are commonly used to describe various complex models that appear in nature, industry, and biology. The equations describing the motion of such fluids are characterized by a non-linear constitutive law...
Preprint
The objective of this paper is twofold. First, we show the existence of global classical solutions to the degenerate inviscid lake equations. This result is achieved after revising the elliptic regularity for a degenerate equation on the associated stream-function, and adapting the method used for construction of classical solutions to the incompre...
Article
Full-text available
In this paper we write, analyze and experimentally compare three different numerical schemes dedicated to the one dimensional barotropic Navier-Stokes equations: a staggered scheme based on the Rusanov one for the inviscid (Euler) system, a staggered pseudo-Lagrangian scheme in which the mesh “follows” the fluid, the Eulerian projection (on a fixed...
Preprint
Full-text available
In this work, we are interested in the numerical simulation of the compressible Navier-Stokes system in the isentropic case, where the pressure is a simple function of the density, namely we fix $ p (\ rho) = a \ rho ^ \ gamma $, with $ a> 0 $ and $ \ gamma> 1. $ The fluid is subjected to the external force $ f $. This work is particularly motivate...
Preprint
Full-text available
In this short note, we prove by simple arguments some functional inequalities in arbitrary space dimensions. We investigate the applications of our results in establishing some appropriate a priori estimates (entropy estimates) on the approximate solution of some models related to fluid dynamics system. In particular , we derive some entropy inequa...
Preprint
In this short note, we prove by simple arguments a new kind of Logarithmic Sobolev inequalities generalizing two known inequalities founded in some papers related to fluid dynamics models (see for instance [6] and [3]). As a by product, we show how our inequality can help in obtaining some important a priori estimates for the solution of the Navier...
Thesis
Full-text available
Cette thèse est consacrée à l'analyse mathématique de quelques modèles hétérogèenesintervenant en mécanique des fluides. En particulier, elle est consacrée à l'étude théoriquedes systèmes d'équations aux dérivées partielles décrivant les modèles principaux quenous présentons dans ce qui suit. En premier temps, nous avons étudié l'écoulementd'un flu...
Thesis
Cette thèse est consacree a l'analyse mathematique de quelques modeles heterogenesintervenant en mecanique des uides. En particulier, elle est consacree a l'etude theoriquedes systemes d'equations aux derivees partielles decrivant les modeles principaux quenous presentons dans ce qui suit. En premier temps, nous avons etudie l'ecoulementd'un uide v...
Article
Full-text available
The aim of this paper is to discuss the issue of global existence of weak solutions of the so called ghost effect system which has been derived recently in [C. D. Levermore, W. Sun, K. Trivisa, SIAM J. Math. Anal. 2012]. We extend the local existence of solution proved in [C.D. Levermore, W. Sun, K. Trivisa, Indiana Univ. J., 2011] to a global exis...
Article
This paper concerns the effect of viscosity on the degenerate lake equation (anelastic limit) when the bottom topography vanishes on the shore. We establish the existence and uniqueness of weak solution for various viscous choices in weighted Sobolev spaces where the weight is assumed to be a power type weight. Our solution is constructed by adapti...

Network

Projects

Projects (2)
Project
Comparison of Finite Volume Schemes for Compressible and barotropic Navier-Stokes equations
Project
This project is a part of my work in post-doctoral position with Boris Haspot, Bernard Di Martino and Yohan benel