4 problems

Nam's coefficient conjecture. The main part of the conjecture is that

Let $E(N,lambda v)$ and $E(N-1,lambda v)$ denote the ground-state energies of the trapped Bose gas with interaction scaling $lambda$, and let $T$ and $v$ satisfy appropriate condit…

Finite-time blow-up conjecture. Solutions with $m\leq m_c$ should be globally defined for all $t\in[0,\infty)$, whereas solutions with $m>m_c$ should blow up at a finite time $T^*$…

Let $\mathfrak p$ denote the operator introduced through the quaternionic formulation of the field equations, and decompose its action into linear and nonlinear parts. The linear p…