This course is an introduction to the mathematical analysis of some classical fluid models called hyperbolic systems of conservation laws. Such systems appear in fluid dynamics, road traffic, electromagnetism, acoustics, and more.

We will present those models and briefly recall their derivation. We wil then proceed with their mathematical analysis and study successively: - linear systems in one dimension, - nonlinear scalar conservation laws in one dimension, - linear and quasi-linear systems in several dimensions.

An important feature of those problems is that generic solutions have discontinuities called shocks which necessitate a specific approach through entropic weak solutions.

The course will be in english.