Lecture notes in fluid mechanics: From basics to the millennium problem/ Laurent Schoeffel 1 Lecture notes in fluid mechanics: From basics to the millennium problem Laurent Schoeffel, CEA Saclay. These lecture notes have been prepared as a first course in fluid mechanics up to the presentation of the millennium problem listed by the Clay Mathematical Institute. Only a good knowledge of classical Newtonian mechanics is assumed. We start the course with an elementary derivation of the equations of ideal fluid mechanics and end up with a discussion of the millennium problem related to real fluids. With this document, our primary goal is to debunk this beautiful problem as much as possible, without assuming any previous knowledge neither in fluid mechanics of real fluids nor i n the mathematical formalism of Sobolev’s inequalities. All these items are introduced progressively through the document with a linear increase in the difficulty. Some rigorous proofs of important partial results concerning the millennium problem are presented. At the end, a very modern aspect of fluid mechanics is covered concerning the subtle issue of its application to high energetic hadronic collisions.
