Joackim Bernier
Junior CNRS researcher (chargé de recherche),
Laboratoire de Mathématiques Jean Leray,
Nantes Université.
Email
joackim.bernier (at) univ-nantes.fr
Address
Laboratoire de Mathématiques Jean Leray
Nantes Université
2 rue de la Houssinière
F-44322 Nantes cedex 3 FRANCE
CV (PDF)
joackim.bernier (at) univ-nantes.fr
Address
Laboratoire de Mathématiques Jean Leray
Nantes Université
2 rue de la Houssinière
F-44322 Nantes cedex 3 FRANCE
CV (PDF)
Main research interests
- Hamiltonian PDEs: almost global existence, almost periodic solutions, dynamics at low regularity.
- Geometrical numerical integration: splitting methods, backward error analysis.
- Regularizing effects of semigroups generated by non-selfadjoint operators.
- Discrete dispersive PDEs: long time behavior, qualitative properties.
Preprints
Papers
- Almost global existence for Hamiltonian PDEs on compact manifolds arXiv
- Infinite dimensional invariant tori for nonlinear Schrödinger equations arXiv
- On alternating-conjugate splitting methods arXiv doi
- Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity arXiv doi
- Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori doi
- Dynamics of quintic nonlinear Schrödinger equations in \(H^{2/5+}(\mathbb{T})\) arXiv doi
- Almost global existence for some nonlinear Schrödinger equations on \(\mathbb{T}^d\) in low regularity doi
- Exponential stability of solutions to the Schrödinger-Poisson equation arXiv doi
- Symmetric-conjugate splitting methods for linear unitary problems doi
- Gains of integrability and local smoothing effects for quadratic evolution equations arXiv doi
- Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects arXiv doi
- Dynamics of nonlinear Klein-Gordon equations in low regularity on \(\mathbb{S}^2\) arXiv doi
- Birkhoff normal forms for Hamiltonian PDEs in their energy space doi
- Long time dynamics for generalized Korteweg-de Vries and Benjamin-Ono equations arXiv doi
- Long-time existence for semi-linear beam equations on irrational tori arXiv doi
- Exact splitting methods for semigroups generated by inhomogeneous quadratic differential operators arXiv doi
- Exact splitting methods for kinetic and Schrödinger equations arXiv doi
- Splitting methods for rotations: application to Vlasov equations hal doi
- Long time behavior of the solutions of NLW on the d-dimensional torus doi
- Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium arXiv doi
- Rational normal forms and stability of small solutions to nonlinear Schrödinger equations arXiv doi
- Smoothing Properties of fractional Ornstein-Uhlenbeck semigroups and null-controllability arXiv doi
- Existence and stability of traveling waves for discrete nonlinear Schrödinger equations over long times arXiv doi
- Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on \(h\mathbb{Z}\) arXiv doi
- Optimality and resonances in a class of compact finite difference schemes of high order arXiv doi
- Verification of 2D × 2D and two-species Vlasov-Poisson solvers hal doi
PhD thesis
- Etude de quelques perturbations d'équations riches en symétries : résonances et stabilités hal