PhD Course Introduction to mathematical fluid dynamics

This is the webpage for a short course on mathematical fluid dynamics in the PhD program in mathematics at the University of Calabria.

This short course provides a rigorous introduction to the mathematical analysis of the Euler and Navier-Stokes equations, the fundamental models for incompressible fluid flow.

Tailored for PhD students in the Phd program  in mathematics, the lectures aim to bridge the gap between classical 20th-century foundations and some of the recent breakthroughs of the 2020s.

A syllabus of the course can be found here. 

Participants are very welcome to pass by my office at DEMACS  from 18-29 May at any time to discuss the material or further questions. Alternatively, please reach out by mail.

Overview of the lecture and material. 

  1. Lecture (19 May). Derivation of the equations and first properties. Notes
  2. Lecture (21 May). Local existence by energy methods and potential singularity formation. Notes
  3. Lecture (22 May). Local well-posedness theory extended.
  4. Lecture (25 May). Beale-Kato-Majda, singularity formation and global 2D flows. Notes

The notes are protected by password and are made available to the course's participants as well as on request.