This page contains some of the mathematical texts I have written. Many of them are not quite finished, and all are heavily laden with mistakes of all kinds. This is ongoing work...
PhD Dissertation
My PhD dissertation (written in English), defended in June 2022, is about the Mathematical Study of Fluids Interacting with a Magnetic Field and can be downloaded here.
Miscellaneous
- Some notes (in French) for a talk about the divergence-free condition in mathematical physics, given in Lyon for the PhD students seminar on the 14th of December 2020. This document introduces the Leray projection in the Euler system, as well as Elsässer variables in magnetohydrodynamics. Here is a french abstract.
- Notes of a talk about some applications of harmonic analyssi to the study of the Euler equations. The talk should have been given in April 2020 at l'Institut Fourier, in Grenoble for the PhD student seminar. However, it has been delayed because of the CoViD19 epidemic.
- Notes (in french) for a short talk about the RAGE theorem and one of its applications to a fast rotation problem in fluid dynamics. The talk was given on June 2019 at the l'ENS Rennes, during a meeting of the 4th year students.
- Some (in french) of my développements I prepared in order to take the french agrégation de Mathématiques selective examination.
- Some mathematical problems (in french) I used for oral examinations in the Lycée du Parc.
Things written for my studies
- My master's thesis' written under the supservision of Francesco Fanelli after a four month long internship. We studied a model of fast rotating magnetohydrodynamics. One of the main chalenges of this work is that we allowed for the viscosity and resistivity to depend continuously on the density
- The report of a six/seven week long internship about a recent isodiametric inequality (2017) for the Steklov eigenvalues. This work was performed at the l'Institut de Mathématiques de l'Université de Neuchâtel under the supervision of Bruno Colbois.
- The report (in french) of a five week long internship on Calderòn-Zygmund theory for singular integral operators, and an application to the uniqueness of the Yudovich solutions for the incompressible Euler equations. This work was done at l'institut Camille Jordan under the supervision of Dragos Iftimie.
- The micro-thesis (in french) I wrote during my agrégation year, as a master's degree is required to take the examination. This work is written in the format used for the oral examinations and is related to the lesson on compactness, under the supervision of Jean-Christophe Breton.