29 citations · 119 across the 11 of their papers we have counts for
15 papers
Dynamics of nonlinear Klein-Gordon equations in low regularity on S^2
Joackim Bernier, Benoît Grébert, Gabriel Rivière
We describe the long time behavior of small non-smooth solutions to the nonlinear Klein-Gordon equations on the sphere S^2. More precisely, we prove that the low harmonic energies…
Birkhoff normal forms for Hamiltonian PDEs in their energy space
Joackim Bernier, Benoît Grébert
We study the long time behavior of small solutions of semi-linear dispersive Hamiltonian partial differential equations on confined domains. Provided that the system enjoys a new n…
Long-time existence for semi-linear beam equations on irrational tori
Joackim Bernier, Roberto Feola, Benoît Grébert +1
We consider the semi-linear beam equation on the d dimensional irrational torus with smooth nonlinearity of order n -- 1 with n 3 and d 2. If 1 is the size of…
Long time solutions for quasi-linear Hamiltonian perturbations of Schrödinger and Klein-Gordon equations on tori
Roberto Feola, Benoît Grébert, Felice Iandoli
We consider quasi-linear, Hamiltonian perturbations of the cubic Schrödinger and of the cubic (derivative) Klein-Gordon equations on the dimensional torus. If …
Long time dynamics for generalized Korteweg-de Vries and Benjamin-Ono equations
Joackim Bernier, Benoît Grébert
We provide an accurate description of the long time dynamics of the solutions of the generalized Korteweg-De Vries (gKdV) and Benjamin-Ono (gBO) equations on the one dimension toru…
Reducibility of Schrödinger equation on a Zoll manifold with unbounded potential
Roberto Feola, Benoît Grébert, Trung Nguyen
In this article we prove a reducibility result for the linear Schrödinger equation on a Zoll manifold with quasi-periodic in time pseudo-differential perturbation of order less or…