7 problems

Global wellposedness conjecture. When $\mu=1$, the equation is globally wellposed: for each $u_0\in\Sigma$ there is a unique global solution…

Factorisation conjecture. One has

General-form conjecture. The coefficients have the form

Let $u(x,t)$ solve the harmonic-oscillator Schrödinger Cauchy problem … with $u_0\in E^1(\tanh 2\alpha,\tanh 2\alpha)$ for some $\alpha>0$. Vemuri's endpoint conjecture. The evolut…

Let $Wf$ be a Wigner function on $\mathbb{R}^{2}$ whose negative part is nonempty and contained in a disc. For a Wigner function $Wf$, denote its negative part by…

For $N\in\mathbb N^*$, let $\mathfrak A_N^{har}$ be the isotropic harmonic-oscillator array, let $\lambda_k^{har}$ denote its $k$-th eigenvalue, and let $m(k,\mathfrak A)$ denote t…

Spectral-bound conjecture. For sufficiently small $\epsilon>0$,