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

I am a CNRS junior research scientist in mathematics, working at IRMAR laboratory, in Rennes, France. I am currently interested in control theory (mostly nonlinear systems), fluid mechanics and boundary layers.

Former student at ENS Ulm, 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 on the analysis of boundary layer models then of Karine Beauchard, on quadratic obstructions to controllability.

Contact

You can contact me by email at first.last@ens-rennes.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.

Research papers
  1. A unified approach of obstructions to small-time local controllability for scalar-input systems (with K. Beauchard)
    preprint, arXiv:2205.14114
  2. A nonlinear forward-backward problem (with A.-L. Dalibard and J. Rax)
    preprint, arXiv:2203.11067
  3. Growth of structure constants of free Lie algebras relative to Hall bases (with K. Beauchard and J. Le Borgne)
    preprint, arXiv:2111.14398
  4. On expansions for nonlinear systems, error estimates and convergence issues (with K. Beauchard and J. Le Borgne)
    Comptes Rendus Mathématique, in press, 2022
  5. 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, 2019
  6. 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
  7. 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
  8. Quadratic obstructions to small-time local controllability for scalar-input systems (with K. Beauchard)
    J. Differential Equations, 264(5):3704-3774, 2018
  9. 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
  10. 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,
  11. 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