3 problems

Let $\mathcal{B}=\{x\in\mathbb{R}^n:|x|\leq 1\}$ be the closed unit ball and consider the exterior problem on $\mathcal{B}^c$: … with $u=0$ on $\partial\mathcal{B}^c$ and initial d…

Let $\Omega\subset\mathbb{R}^3$ be the exterior domain of a smooth, compact, strictly convex obstacle, and consider the defocusing nonlinear Schrödinger equation with Dirichlet bou…

Exterior-domain critical-curve conjecture. The curve produced by $\partial\mathcal{C}$ is a critical curve separating the exponent pairs for which fast-decaying exterior-domain sol…