3 problems

Sharp regularity threshold conjecture. There exists $s_0\in\mathbb R$ such that the equation is well-posed in $H^s$ if and only if $s\geq s_0$.

Extension and renormalization conjecture. Theorems 5 and 6 should extend to $\alpha>1$, and, after suitable renormalizations, even to some values of $\alpha\leq1$.

Extension conjecture. It should be possible to extend Theorem 6 to every $\alpha>1$ by adapting a more involved resolution ansatz.