  In this article we study the problem of nonlinear Landau damping for the
Vlasov-Poisson equations on the torus. As our main result we show that for
perturbations initially of size $\epsilon>0$ and time intervals
$(0,\epsilon^{-N})$ one obtains nonlinear stability in regularity classes
larger than Gevrey $3$, uniformly in $\epsilon$. As a complementary result we
construct families of Sobolev regular initial data which exhibit nonlinear
Landau damping. Our proof is based on the methods of Grenier, Nguyen and
Rodnianski.
