Preprints

• Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori [arXiv]
  with Nicolas Camps.
• Exponential stability of solutions to the Schrödinger-Poisson equation [arXiv]
  with Nicolas Camps, Benoît Grébert and Zhiqiang Wang.
• Dynamics of quintic nonlinear Schrödinger equations in \(H^{2/5+}(\mathbb{T})\) [arXiv]
  with Benoît Grébert and Tristan Robert.
• Almost global existence for some nonlinear Schrödinger equations on \(\mathbb{T}^d\) in low regularity [arXiv]
  with Benoît Grébert, to appear in Annales de l'Institut Fourier.

Papers

• Symmetric-conjugate splitting methods for linear unitary problems [doi] (open access)
  Bit Numer Math, 63, 58 (2023), with Sergio Blanes, Fernando Casas and Alejandro Escorihuela-Tomàs.
• Gains of integrability and local smoothing effects for quadratic evolution equations [arXiv,doi]
  Journal of Functional Analysis, Volume 285, Issue 10, 15 November 2023, 110119 with Paul Alphonse.
• Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects [arXiv,doi]
  Annales Scientifiques de l'ENS, 4 e série, t. 56, 2023, p. 323 à 382, with Paul Alphonse.
• Dynamics of nonlinear Klein-Gordon equations in low regularity on \(\mathbb{S}^2\) [arXiv, doi]
  Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 40 (2023), no. 5, pp. 1009–1049 with Benoît Grébert and Gabriel Rivière.
• Birkhoff normal forms for Hamiltonian PDEs in their energy space [doi] (open access)
  Journal de l’Ecole polytechnique — Mathématiques, Tome 9 (2022), pp. 681-745, with Benoît Grébert.
• Long time dynamics for generalized Korteweg-de Vries and Benjamin-Ono equations [arXiv,doi]
  Archive for Rational Mechanics and Analysis, (2021) with Benoît Grébert.
• Long-time existence for semi-linear beam equations on irrational tori [arXiv,doi]
  Journal of Dynamics and Differential Equations, (2021), with Roberto Feola, Benoît Grébert and Felice Iandoli.
• Exact splitting methods for semigroups generated by inhomogeneous quadratic differential operators [arXiv,doi]
  Foundations of Computational Mathematics (2021).
• Exact splitting methods for kinetic and Schrödinger equations [arXiv,doi]
  Journal of Scientific Computing, 86 (10) (2021), with Nicolas Crouseilles and Yingzhe Li.
• Splitting methods for rotations: application to Vlasov equations [hal,doi]
  SIAM Journal on Scientific Computing 2020 42:2, A666-A697, with Fernando Casas and Nicolas Crouseilles.
  Bonus: a note to detail the microlocal estimates [hal].
• Long time behavior of the solutions of NLW on the d-dimensional torus [doi] (open access)
  Forum of Mathematics, Sigma (2020), Vol. 8, e12, 26 pages, with Erwan Faou and Benoît Grébert.
• Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium [arXiv,doi]
  Kinetic and Related Models, February 2020, 13 (1), 129-168 with Michel Mehrenberger.
• Rational normal forms and stability of small solutions to nonlinear Schrödinger equations [arXiv,doi]
  Annals of PDE 6, 14 (2020), with Erwan Faou and Benoît Grébert.
• Smoothing Properties of fractional Ornstein-Uhlenbeck semigroups and null-controllability [arXiv,doi]
  Bulletin des Sciences Mathématiques, Volume 165, 2020, 102914, with Paul Alphonse.
• Existence and stability of traveling waves for discrete nonlinear Schrödinger equations over long times [arXiv,doi]
  SIAM Journal on Mathematical Analysis, 2019, 51(3), 1607–1656 with Erwan Faou.
• Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on \(h\mathbb{Z}\) [arXiv,doi]
  Discrete & Continuous Dynamical Systems-A, 2019, 39(6):3179-3195.
• Optimality and resonances in a class of compact finite difference schemes of high order [arXiv,doi]
  Calcolo (2019) 56: 12.
• Verification of 2D × 2D and two-species Vlasov-Poisson solvers [hal,doi]
  ESAIM: ProcS, 2018, 63:78-108, with Yann Barsamian, Sever Hirstoaga and Michel Mehrenberger.

PhD thesis

• Etude de quelques perturbations d’équations riches en symétries : résonances et stabilités [hal].