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-now)

Post-doc
Thomas Perrin (2024-now)
Research papers
  1. An obstruction to small-time local controllability for a bilinear Schrödinger equation (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)
    preprint, arXiv:2203.11067
  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. 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
  2. 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
  3. Obstructions quadratiques à la contrôlabilité, de la dimension finie à la dimension infinie, Séminaire Laurent Schwartz - EDP et applications, 2016-2017, Exp. No. 16