8 problems

Wave maximizer conjecture. The set of maximizers for which equality holds in the sharp wave Strichartz inequality coincides with the set of initial data of solutions in the orbit o…

For an integer $n\geq 1$, set $p=2+4/n$. Let $f_*$ be the Gaussian … and let $u_*(t,x)=\mathrm{e}^{-\mathrm{i}t\Delta}f_*(x)$ be the corresponding solution of the Schrödinger equat…

Let $(q,r)$ be a Schrödinger-admissible pair with $4<q<\finite$ and $gamma=1/q$. Let $A_{q,r}$ denote the sharp Airy–Strichartz constant, let $\widetilde A_{q,r}$ denote the Frank–…

Let $(q,r)$ be an admissible Strichartz pair in dimension $d=1$, and consider the corresponding Schrödinger Strichartz ratio and its extremizers. Universal Gaussian extremizer conj…

Gaussian maximizer conjecture. The maximizers for the paraboloid Strichartz inequality are exactly the Gaussian-type functions $g\in\mathcal{G}$. This conjecture has been confirmed…

For the classical Strichartz inequality corresponding to the case $\alpha=2$, let an extremal be a nonzero function attaining equality in the inequality. Gaussian extremals conject…

Optimal-constant conjecture. The optimal constant should be

Conjecture. The Hessian of the $m$-th mode restricted to the real subspace has at least $m$ positive eigenvalues.