TY - JOUR
T1 - On the fourth order Schrödinger equation in three dimensions
T2 - Dispersive estimates and zero energy resonances
AU - Erdoğan, M. Burak
AU - Green, William R.
AU - Toprak, Ebru
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2021/1/15
Y1 - 2021/1/15
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jde.2020.08.019
DO - 10.1016/j.jde.2020.08.019
M3 - Article
AN - SCOPUS:85091040220
SN - 0022-0396
VL - 271
SP - 152
EP - 185
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -