5 problems

Consider all solutions of the five-dimensional energy-critical wave equation satisfying the fixed-center, comparable-scale concentrating multi-bubble asymptotic assumptions for $K$…

Fix spatial centers $z_1,\ldots,z_K\in\mathbb{R}^5$ and let $Eq(F)$ be the algebraic equilibrium set governing the rescaled modulation dynamics of the corresponding multi-bubble so…

Let $(u,\partial_tu)$ be a $K$-bubble solution of the five-dimensional energy-critical wave equation in the fixed-center, comparable-scale concentrating regime. Let…

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…

Consider general blow-up solutions of the nonlinear Schrödinger equation, without imposing the special pseudo-conformal multi-bubble form. Merle–Raphaël multi-bubble decomposition…