Frédéric Marbach
arXiv · Google Scholar · HAL · RG
About me

I am a CNRS junior research scientist in mathematics, working at ENS Paris. I am currently interested in nonlinear control theory, fluid mechanics and boundary layers.

I wrote my PhD thesis under the supervision of Jean-Michel Coron on control in fluid mechanics, defended in September 2016. I was then a post-doc student of Anne-Laure Dalibard and Karine Beauchard. I worked for 5 years at IRMAR laboratory, in Rennes, France.

Contact

You can contact me by email at first.last@cnrs.fr

Dear editors, due to my personal conviction for open science and an always increasing number of review demands, I will prioritize reviewing papers for diamond open-access journals starting January 2022.

Students
PhD
Mégane Bournissou (2019-2022)
Théo Gherdaoui (2022-2025)

Post-doc
Thomas Perrin (2024-now)
Research papers
  1. Small-time local control of a Schrödinger equation: a negative and a positive quadratic result (with K. Beauchard and T. Perrin)
    preprint, arXiv:2501.03882
  2. Control theory and splitting methods (with K. Beauchard and A. Laurent)
    preprint, arXiv:2407.02127
  3. A family of interpolation inequalities involving products of low-order derivatives
    preprint, arXiv:2306.06668
  4. A unified approach of obstructions to small-time local controllability for scalar-input systems (with K. Beauchard)
    preprint, arXiv:2205.14114
  5. Linear and nonlinear parabolic forward-backward problems (with A.-L. Dalibard and J. Rax)
    MEMS, vol 25, 2026
  6. Growth of structure constants of free Lie algebras relative to Hall bases (with K. Beauchard and J. Le Borgne)
    Journal of Algebra, 612:281-378, 2022
  7. On expansions for nonlinear systems, error estimates and convergence issues (with K. Beauchard and J. Le Borgne)
    Comptes Rendus Mathématique, 361:97-189, 2023
  8. Controllability of the Navier-Stokes equation in a rectangle with a little help of a distributed phantom force (with J.-M. Coron, F. Sueur and P. Zhang)
    Annals of PDE, 5(17), 2019
  9. Unexpected quadratic behaviors for the small-time local null controllability of scalar-input parabolic equations (with K. Beauchard)
    J. Mathématiques Pures et Appliquées, 136:22-91, 2020
  10. High frequency analysis of the unsteady Interactive Boundary Layer model (with A.-L. Dalibard, H. Dietert, D. Gérard-Varet)
    SIAM J. Mathematical Analysis, 50(4):4203-4245, 2018
  11. Quadratic obstructions to small-time local controllability for scalar-input systems (with K. Beauchard)
    J. Differential Equations, 264(5):3704-3774, 2018
  12. Small-time global exact controllability of the Navier-Stokes equation with Navier slip-with-friction boundary conditions (with J.-M. Coron and F. Sueur)
    J. European Mathematical Society, 22(5):1625-1673, 2020
  13. An obstruction to small-time local null controllability for a viscous Burgers' equation
    Annales Scientifiques de l'École Normale Supérieure, 51(5):1129-1177, 2018,
  14. Small-time global null controllability for a viscous Burgers' equation despite the presence of a boundary layer
    J. Mathématiques Pures et Appliquées, 102(2):364–384, 2014
Conference communications
  1. Nonlinear forward-backward problems (with A.-L. Dalibard and J. Rax)
    The Abel Symposium, June 2023, pp. 53-72
  2. On the controllability of the Navier-Stokes equation in a rectangle with a little help of a distributed phantom force (with J.-M. Coron, F. Sueur and P. Zhang)
    JEDP 2018, Obernai
  3. On the controllability of the Navier-Stokes equation in spite of boundary layers (with J.-M. Coron and F. Sueur)
    RIMS Kôkyûroku, 2058:162-180, 2018
  4. Obstructions quadratiques à la contrôlabilité, de la dimension finie à la dimension infinie, Séminaire Laurent Schwartz - EDP et applications, 2016-2017, Exp. No. 16