4 papers · 1 filter
On weakly turbulent solutions to the perturbed linear Harmonic oscillator
Erwan Faou, Pierre Raphael
We introduce specific solutions to the linear harmonic oscillator, named bubbles. They form resonant families of invariant tori of the linear dynamics, with arbitrarily large Sobol…
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…
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…
Collision of almost parallel vortex filaments
Valeria Banica, Erwan Faou, Evelyne Miot
We investigate the occurrence of collisions in the evolution of vortex filaments through a system introduced by Klein, Majda and Damodaran [KMD95] and Zakharov [Z88,Z99]. We first…