We prove the existence of time-quasi-periodic solutions of the incompressible Euler
equation on the three-dimensional torus T 3, with a small time-quasi-periodic external force …

We prove an abstract theorem giving a〈 t〉 ϵ bound (for all ϵ> 0) on the growth of the
Sobolev norms in linear Schrödinger equations of the form i ψ= H0ψ+ V (t) ψ as t→∞. The …

In this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time
dependent PDEs on the torus∂ t u+ ζ⋅∂ x u+ a (ω t, x)⋅∂ xu= 0, x∈ T d, ζ∈ R d, ω∈ R ν …

We prove an abstract result giving a $\langle t\rangle^{\epsilon} $ upper bound on the
growth of the Sobolev norms of a time dependent Schr\" odinger equation of the form …

We consider a class of linear time dependent Schrödinger equations and quasi-periodically
forced nonlinear Hamiltonian wave/Klein Gordon and Schrödinger equations on arbitrary flat …

Growth of Sobolev norms for unbounded perturbations of the Schrödinger equation on flat tori -
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We prove reducibility of a transport equation on the d-dimensional torus T^ d T d with a time
quasiperiodic unbounded perturbation. As far as we know, this is one of the few reducibility …

We prove that a linear d-dimensional Schrödinger equation on Rd with harmonic potential|
x| 2 and small t-quasiperiodic potential i∂ tu−∆ u+| x| 2u+ εV (tω, x) u= 0, x∈ Rd reduces to …

We study the reducibility of a linear Schrodinger equation subject to a small unbounded
almost periodic perturbation which is analytic in time and space. Under appropriate …

We consider the cubic nonlinear Schrödinger equation on 2-dimensional irrational tori. We
construct solutions which undergo growth of Sobolev norms. More concretely, for every s> 0 …