Introduction to Compressible fluids: Part 1 (Weak Solutions) and Part II (Strong Solutions)

Dates and time: January 20th, 2025 - March 18th, 2025 from 10:30 am to 12:30 pm.

This is an introductory course on Compressible Navier-Stokes equations, spanning 20 hours (2 hours per week over 10 weeks).

The first part of the course (5 weeks: 10 hours) focuses on weak solutions for compressible fluids.

We will prove the existence theory of weak solutions (à la P.L. Lions and E. Feireisl) through the following steps: the continuity equation with dissipation, the vanishing viscosity limit, and the artificial pressure limit. The second part of the course (5 weeks: 10 hours) covers strong solutions for compressible fluids. We will establish the existence and uniqueness of strong solutions, considering both local in time for large data and global in time for small data. Additionally, we will introduce the concept of relative energy, which helps establish weak-strong uniqueness.