Scattering theory below energy for the cubic fourth-order Schrödinger equation

Details Scattering theory below energy for the cubic fourth-order Schrödinger equation Scattering theory below energy for the cubic fourth-order Schrödinger equation

2009-07-29

arxiv.org/abs/0907.5047v2

Mathematics

Analysis of PDEs

33pages

Scientific paper

We investigate the global existence and scattering for the Fourth-order
Schr\"{o}dinger equation in the low regularity space $H^s(\R^n)$, $s<2$. We
provide an alternative approach to obtain a new Morawetz interactive estimate
and extend the range of the dimension of the interactive estimate in Pausader
\cite{P08} by modifying a tensor product method appeared in \cite{CGT}.

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