37 citations · 110 across the 23 of their papers we have counts for
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math.AP2021
Gains of integrability and local smoothing effects for quadratic evolution equations
Paul Alphonse, Joackim Bernier
We characterize geometrically the semigroups generated by non-selfadjoint quadratic differential operators enjoying local smoothing effects and providing ga…
math.AP2021
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…
math.AP2021
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…