We study the fourth order Schrödinger operator H=(−Δ)2+V for a short range potential in three space dimensions. We provide a full classification of zero energy resonances and study the dynamic effect of each on the L1→L∞ dispersive bounds. In all cases, we show that the natural [Formula presented] decay rate may be attained, though for some resonances this requires subtracting off a finite rank term, which we construct and analyze. The classification of these resonances, as well as their dynamical consequences differ from the Schrödinger operator −Δ+V.
ASJC Scopus subject areas
- Applied Mathematics