3 problems

Ground state conjecture. The solution extends uniquely to a global solution $u\in C(\mathbb{R}:\dot{H}^1(\mathbb{R}^d))$ of

Let $d\geq 3$, let $I$ be the lifespan interval, and let $u:I\times\mathbf{R}^{d}\to\mathbf{C}$ solve the focusing energy-critical nonlinear Schrödinger equation with…

Minimal kinetic-energy conjecture. If $E_*<\|\nabla W\|_2$, then