4 problems

Consider the periodically forced Dirac equation with mass $m=1$, and let $M^n$ denote its $n$-period propagator. For $\beta>0$, write…

Weinstein's small-data decay conjecture. Solutions with sufficiently small initial conditions satisfy

Sharp decay conjecture. The estimate

Let $H_0=-\Delta+V_0(x)$, where $V_0$ is a real positive, slowly decreasing potential satisfying the assumptions described above, and consider the associated time evolution and its…