arXiv subjects

Haigen Wu

Publications and source records attributed to Haigen Wu.

2 recordsLinked to original sources

arXiv2013

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

We investigate the global existence and scattering for the cubic fourth-order Schrödinger equation $iu_t+Δ^2u+|u|^2u=0$ in the low regularity space $H^s(\R^n)$ with $s<2$. We provide an alternative approach to obtain a new interaction Morawetz 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}. We combine interaction Morawetz estimates, energy increments for the I-method to prove the result.

math.AP↗

arXiv2008

On the Real Analyticity of the Scattering Operator for the Hartree Equation

In this paper, we study the real analyticity of the scattering operator for the Hartree equation $ i\partial_tu=-Δu+u(V*|u|^2)$. To this end, we exploit interior and exterior cut-off in time and space, and combining with the compactness argument to overcome difficulties which arise from absence of good properties for the nonlinear Klein-Gordon equation, such as the finite speed of propagation and ideal time decay estimate. Additionally, the method in this paper allows us to simplify the proof of analyticity of the scattering operator for the nonlinear Klein-Gordon equation with cubic nonlinearity in Kumlin.

math.AP↗