37 citations · 37 across the 2 of their papers we have counts for
4 papers
Exact splitting methods for kinetic and Schr{ö}dinger equations
Joackim Bernier, Nicolas Crouseilles, Yingzhe Li
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{ö}dinger type…
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…
Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium
Joackim Bernier, Michel Mehrenberger
The asymptotic behavior of the solutions of the second order linearized Vlasov-Poisson system around homogeneous equilibria is derived. It provides a fine description of some nonli…
Rational normal forms and stability of small solutions to nonlinear Schrödinger equations
Joackim Bernier, Erwan Faou, Benoit Grebert
We consider general classes of nonlinear Schrödinger equations on the circle with nontrivial cubic part and without external parameters. We construct a new type of normal forms, na…