6 problems

Let $k>3/2$. In temporal gauge $A_0=0$, let … be the Banach space of Cauchy data $(A^{\operatorname{Cau}},\dot A^{\operatorname{Cau}},\Psi^{\operatorname{Cau}})$, and let…

Slow-dispersion conjecture. For every $\varepsilon>0$, there exists a choice of $\nu(t)$ such that the $L^1\to L^\infty$ decay rate is no faster than $t^{-\varepsilon}$; more preci…

Let $p$ be the coefficient in the one-dimensional Dirac system considered in the paper, and let $a_1$ denote the first coefficient from the asymptotic expansion of the norming cons…

The equation … with initial data $\psi(0,\cdot)=\psi_0\in H^s(\mathbb{R}^3)$, is the Yukawa-type equation under consideration. Dirac–Klein–Gordon origin conjecture. As in the Maxwe…

Petrat–Tumulka conjecture. Interacting systems of this form with general non-vanishing potentials that lead to interaction between the particles are excluded, because they violate…

Let $D$ be the Euclidean Dirac operator on $\mathbb{R}^{n}$, and let $u$ be a solution of … Assume that $u$ has finite relative Morse index. Conjecture. Such solutions should vanis…