37 citations · 39 across the 4 of their papers we have counts for
8 papers · 1 filter
Almost global existence for some nonlinear Schr{ö}dinger equations on in low regularity
Joackim Bernier, Benoît Grébert
We are interested in the long time behavior of solutions of the nonlinear Schr{ö}dinger equation on the -dimensional torus in low regularity, i.e. for small initial data in the…
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…
Exact splitting methods for semigroups generated by inhomogeneous quadratic differential operators
Joackim Bernier
We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential operators. More precisely, we…
Long time behavior of the solutions of NLW on the d-dimensional torus
Joackim Bernier, Erwan Faou, Benoit Grebert
We consider the non linear wave equation (NLW) on the d-dimensional torus with a smooth nonlinearity of order at least two at the origin. We prove that, for almost any mass, small…