4 problems

A localized solution is a spatially localized solution, and regularity in space refers to the spatial regularity assumed in the surrounding discussion. A weakly localized solution…

Consider the $d$-dimensional nonlinear Schrödinger equation with periodic boundary conditions … where $V*$ denotes convolution with the potential $V$. Bourgain's conjecture. Full-d…

Below-ground-state almost-periodic-solution conjecture. There does not exist a nonzero almost periodic solution $u$ to $(1.1)$ satisfying

Let $\dot{\mathcal H}^1$ be the wave-map energy space, and let an energy-class solution be a restriction of a maximal Cauchy development to a subinterval. Such a solution…