Conjecture on delayed blowup under dispersion or nonlinearity management

Let $u_0 otin H^1({\mathbb R}^d)$ such that the solution to the focusing nonlinear Schrödinger equation with $u(0,x)=u_0(x)$ blows up at some time $T>1$. The dispersion-managed or nonlinearity-managed solution with the same initial datum is said to be the corresponding managed solution.

Delayed-blowup conjecture. The corresponding solution of either managed model does not blow up in $[0,T]$; thus, blowup can be delayed by dispersion or nonlinearity management.

This conjecture formalizes the observed stabilization effect of the managed models and is proposed as a target for future rigorous analysis. The supplied text does not state whether it has been resolved.