3 problems

Consider the critical focusing nonlinear Schrödinger equation in one spatial dimension and its standing-wave blow-up solutions. The generalized root space of the linearized operato…

Stable-manifold conjecture. Such initial data are globally well-posed under the nonlinear Schrödinger dynamics if and only if $u_0\notin\mathcal{W}^s(0)$.

Let $X$ be a complex manifold endowed with a Riemannian metric, and let $f\colon X\to X$ be an automorphism acting hyperbolically on an invariant compact subset $K\subset X$. For…