4 problems

Let the radial nonlinear Schrödinger equation generate a dispersive shock wave (DSW) from an initial density jump of size $\rho_b$, and let the cavitation threshold for the one-dim…

Let $M^-_3(\lambda,\infty)$ denote the lower cubic supremum at infinite cutoff, and let $\nu_1^{A,-}\approx0.1923$. Lower cubic-supremum conjecture. The numerical investigations su…

Let $M_3(\lambda,c_0)$ be the cubic supremum, and let $c_1(\lambda)$ be a threshold such that $M_3(\lambda,c_0)=M_3(\lambda,c_1)$ for all $c_0\geq c_1(\lambda)$. For…

Let $G$ be the energy function and let $M_2(\lambda,c_0)$ denote the corresponding supremum, with parameters $\lambda>0$ and $c_0>0$. Quadratic-supremum conjecture. For all…