Mathematics – Analysis of PDEs
Scientific paper
2009-06-18
Mathematics
Analysis of PDEs
46 pages
Scientific paper
We investigate the focusing $\dot H^{1/2}$-critical nonlinear Schr\"{o}dinger equation (NLS) of Hartree type $i\partial_t u + \Delta u = -(|\cdot|^{-3} \ast |u|^2)u$ with $\dot H^{1/2}$ radial data in dimension $d = 5$. It is proved that if the maximal life-span solution obeys $\sup_{t}\big\||\nabla|^{{1/2}}u\big\|_2 < \frac{\sqrt{6}}{3} \big\||\nabla|^{{1/2}}Q\big\|_2$, where $Q$ is the positive radial solution to the elliptic equation(\ref{e14}). Then the solution is global and scatters.
Gao Yanfang
Miao Changxing
Xu Guixiang
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