8 problems

Consider the pseudoconformal blow-up solutions of the self-dual Chern–Simons–Schrödinger equation and the rotational instability described by the phase rotation and subsequent spre…

Let $K\geq 2$, let $z_1,\ldots,z_K\in\mathbb{R}^5$ be pairwise distinct, and consider a global forward-in-time solution of the five-dimensional focusing energy-critical wave equati…

Let $\mathcal{F}^+$ denote the set of initial data whose corresponding solutions have the relevant stable blow-up behavior. Openness conjecture. The set $\mathcal{F}^+$ is open. Th…

Consider the post-adiabatic regime of the one-dimensional damped nonlinear Schrödinger equation, where the dynamics are described by the linear Schrödinger equation … Let $M_c$ den…

Consider the damped nonlinear Schrödinger equation … Here the collapsing core is the localized part of the solution near blow-up, and dissipation removes mass from this core. Influ…

Let $u$ be a stable blow-up solution of the $L^2$-critical generalized Hartree equation, with blow-up time $T$, spatial dimension $d$, scale $L(t)$, center $x(t)$, phase parameter…

Let $Q$ be the rescaled profile and let $H[Q]$ denote its rescaled Hamiltonian. The criticality index is $s_c=1$ in the energy-critical case. Constancy conjecture. The rescaled Ham…

Consider the focusing cubic wave equation on $\mathbb{R}^{1+3}$ and a self-similar solution. Applying time translation and conformal inversion produces a two-parameter family of so…