Study of a few problems concerning plasma physics and fluid mechanics

The works presented in this thesis deal with solving partial differential equations concerning the laser-plasma interaction and some issues in fluid mechanics. All these works involve significant research in the modelization field: the approximation of oscillating hyperbolic systems, the simulation of Zakharov-type systems involving the Raman effect, Hele-Shaw models and gigantic micelles models. They also tackles theoretical issues like the existence and the uniqueness of solutions, the stability or instability of solitary waves, the optimal control, error estimation and model convergency