7 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…

Generic wave control conjecture. Generically with respect to the lengths $(\ell_i)_{i=1,\dots,N}$, (GGCC) is a necessary and sufficient condition for the internal control of the wa…

Avdonin–Zhao's watershed conjecture. The watershed description of Avdonin and Zhao provides the optimal time for the observation and control of the free wave equation on a graph.

Fractal-time local smoothing conjecture. For every $s>s_E(p,q)$, there exists a constant $C_{s,p,q}>0$ such that

Let $d \geq 2$, $q \in (2,\infty)$, and $r \in [2,\infty)$ satisfy … Let $\beta_{d/2}(q,r)$ denote the exponent appearing in the conjectured estimate, and let the estimate … holds…

Let $\Sigma_0$ be a complete $2$-ended asymptotically flat Cauchy hypersurface in a Kerr spacetime with $0<|a|<M$, and let $\psi$ solve the linear wave equation … The relevant assu…

Let $\Sigma_0$ be a Cauchy hypersurface in a subextremal rotating Kerr spacetime, and let $\psi$ solve the linear wave equation … Assume the initial data on $\Sigma_0$ are smooth a…