On some heteregenous model in fluid mechanics

Résumé : This thesis is devoted to the mathematical analysis of some heterogeneous models raised by fluid mechanics. In particular, it is devoted to the theoretical study of partial differential equations used to describe the main models that we present in the following. Firstly, we are interested to study the motion of a incompressible newtonien fluids in a basin with degenerate topography. The mathematical model studied derives from 3d-incompressible Navier-Stokes equations. We are interested to prove that the Cauchy problem associated is well posed. The second part in my thesis is devoted to study a model that arises from dispersive Navier-Stokes equations (that includes dispersive corrections to the classical compressible Navier-Stokes equations). Our model is derived from the last model assuming that the Mach number is very low. The obtained system is called ghost effect system, which is so named because it cannot be derived from the Navier-Stokes system of gas dynamics, while it can be derived from kinetic theory. The main goal of this part is to extend a result concerning the local existence of strong solution to a global in time existence of weak solutions. Finally, we are interested to prove certain functional inequalities who have noticeable interest in solving mathematical systems linked to fluid mechanics.
Type de document :
Thèse
Mathematics [math]. Université de Grenoble Alpes; Université libanaise, 2016. English
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https://hal.archives-ouvertes.fr/tel-01622673
Contributeur : Bilal Al Taki <>
Soumis le : lundi 4 décembre 2017 - 11:51:42
Dernière modification le : jeudi 7 décembre 2017 - 01:12:30

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  • HAL Id : tel-01622673, version 1

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Bilal Al Taki. On some heteregenous model in fluid mechanics. Mathematics [math]. Université de Grenoble Alpes; Université libanaise, 2016. English. 〈tel-01622673〉

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