About me

I am currently a postdoctoral researcher at the Laboratoire de Mathématiques et Modélisation d'Évry (LaMME), working under the supervision of Mickaël Latocca and Thomas Alazard.

Before that, I prepared my PhD at Université Paris Cité, under the supervision of Cosmin Burtea and David Gérard-Varet. I was supported by the MathInParis2020 Cofund doctoral programme of the Fondation Sciences Mathématiques de Paris.

For more details, you can consult my 📄 resume .

✉️ marcel(dot)zodji(at)univ-evry(dot)fr
☎️ +33 (0)1 64 85 35 60

🔎 Research overview

My doctoral research focuses on free boundary problems for models describing the flow of fluid mixtures. The constituents of the mixture are assumed to be immiscible (for instance, gas bubbles in a liquid) and are separated by one or more interfaces of zero thickness. The objective is to investigate the propagation of the regularity of these interfaces over time; this involves establishing the well-posedness of the underlying models. We employ Hoff-type energy estimates together with Lagrangian changes of variables and a number of harmonic analysis tools.

Currently, I study a fluid–structure interaction model, and the regularity of Lagrangian trajectories for solutions of the incompressible Euler equations. Both projects draw on the theory of Littlewood–Paley and on microlocal analysis.

🌊Euler and Navier–Stokes equations ⚪⚫Two-fluid model Free boundary icon Free boundary problem Bubbly liquid icon Bubbly liquid
🟢 ORCID 📄 ArXiv 📁 HAL

🤝 Mentoring

I dedicate roughly an hour per week to supporting high school students with their maths exercises. Most of the time, they are motivated, and a small amount of help is enough to help them feel more at ease with mathematics. I warmly encourage others to volunteer as well; you can find many opportunities here.

📚 Research

Preprint
  • 4
    Global-in-time Discontinuous Solutions for the Two-Phase Model of Compressible Fluids
    with Density-Dependent Viscosity, 2025.
    Submitted — ArXiv · HAL
Peer-reviewed articles
  • 3
    A well-posedness result for the compressible two-fluid model with density-dependent viscosity, 2025.
    J. Math. Fluid Mech.
    Journal · ArXiv · HAL
  • 2
    Global-in-time well-posedness of the compressible Navier–Stokes equations with striated density, 2025.
    Rev. Mat. Iberoam. (with X. Liao).
    Journal · ArXiv · HAL
  • 1
    Discontinuous solutions for the Navier–Stokes equations with density-dependent viscosity, 2024.
    Ann. Inst. H. Poincaré C.
    Journal · ArXiv · HAL
Theses
  • 4
    PhD thesis: Qualitative study of the interface between two compressible immiscible fluids, 2025.
    IMJ-PRG, Université Paris Cité. (HAL)
    Supervisors: Cosmin Burtea, David Gérard-Varet.
    Advisor: Helge Dietert.
  • 3
    Master thesis: Singular pressures in the mechanics of compressibles dynamics, 2021.
    IMJ-PRG, Université Paris Cité. (PDF)
    Supervisors: Cosmin Burtea, David Gérard-Varet.
    Advisor: Julien Guillod.
  • 2
    Master thesis: A result for transport equations and conservation with diffusion, 2020.
    IMSP, Université d'Abomey Calavi. (PDF)
    Supervisor: Nicolas Depauw (Nantes Université).
  • 1
    Undergraduate thesis: Cauchy Lipschitz theorem, 2018. (with Edah Franco Roberto)
    IMSP, Université d'Abomey Calavi. (PDF)
    Supervisor: Leadi Liamidi.

🎤 Talks & presentations

  • 14
    Nov. 12, 2025 – Online talk, School of Mathematical Sciences, Beijing Normal University, China.
  • 13
    Oct. 27–31, 2025 – Poster, Workshop “End of CRISIS”, Marseille (CIRM), France.
  • 12
    Sept. 21–26, 2025 – Workshop “MathFlows' 25”, Porquerolles, France.
  • 11
    June 23–27, 2025 – Poster, Summer school “Particles in Flow”, Bonn, Germany.
  • 10
    June 17, 2025 – PhD thesis defense, IMJ-PRG, Université Paris Cité.
  • 9
    April 15, 2025 – Séminaire MAC, Institut de Mathématiques de Toulouse, France.
  • 8
    March 20, 2025 – Séminaire de l'équipe d'Analyse et EDP, LaMME, Université d'Évry.
  • 7
    Sept. 2–4, 2024 – Meeting on Differential Equations in Ancona, Ancona, Italy.
  • 6
    Feb. 23, 2024 – Séminaire EDPs2, LAMA, Université Savoie Mont Blanc.
  • 5
    Jan. 31, 2024 – Séminaire des doctorant.es du LJLL, Paris.
  • 4
    Jan. 8–9, 2024 – Poster, “Journées de lancement de l'ANR BOURGEONS”, Paris.
  • 3
    Nov. 16–17, 2023 – Conference “Maths pour la Géophysique”, Amiens.
  • 2
    July 25, 2023 – Working group “Nonlinear PDE”, Karlsruhe Institute of Technology, Germany.
  • 1
    March 22, 2023 – Poster, “Journées Jeunes EDPistes”, Tours, France.

📘 Teaching

Université d'Évry-Val-d'Essonne
  • 2025–2026 – Tutorials
    • Langage mathématique (L1 – Portail Math-Info, lectures by Abdelmejid Bayad).
Université Paris Cité
  • 2024–2025 – Tutorials
    • Elementary Mathematics (L1 Physics, lectures by Iro Bartzia).
    • Mathematics for Biologists (L2 Bio, lectures by Cosmin Burtea).
    • Discrete Probabilities (L2 MIASHS, lectures by Noé Cuneo).
    • Mathematics for Engineers (L2 CUPGE, lectures by Olivier Bokanowski).
  • 2023–2024 – Tutorials
    • Discrete Probabilities (L2 MIASHS, lectures by Noé Cuneo).
    • Mathematics and Applications to Life Sciences (L1 PASS, lectures by Denis Perrot).
  • 2022–2023
    • Tutorial: Discrete Probabilities (L2 MIASHS, lectures by Benoît Laslier).
    • Computer lab sessions: Office Software and Internet Tools (L1 Maths-IT).
  • 2021–2022
    • Tutorial: Discrete Probabilities (L2 MIASHS, lectures by Benoît Laslier).
    • Computer lab sessions: Office Software and Internet Tools (L1 Maths-IT).