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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…