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arXiv · 1905.02890

On the Fourth order Schrödinger equation in three dimensions: dispersive estimates and zero energy resonances

Burak Erdogan·William R. Green·Ebru Toprak
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Abstract

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 $L^1\to L^\infty$ dispersive bounds. In all cases, we show that the natural $|t|^{-\frac34}$ 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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Burak Erdogan, William R. Green, Ebru Toprak. 2019-05-07. On the Fourth order Schrödinger equation in three dimensions: dispersive estimates and zero energy resonances. https://doi.org/10.1016/j.jde.2020.08.019

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