Guixiang Xu · wovepaper

most citedGlobal well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data

84 citations · 84 across the 1 of their papers we have counts for

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Scattering for the focusing $H ˙^{1/2}$ -critical Hartree equation with radial data

Yanfang Gao, Changxing Miao, Guixiang Xu

We investigate the focusing $H ˙^{1/2}$ -critical nonlinear Schrödinger equation (NLS) of Hartree type $i \partial_{t} u + Δ u = - (∣ \cdot ∣^{- 3} * ∣ u ∣^{2}) u$ with $H ˙^{1/2}$ radi…

math.AP2008★ 126 cited

Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case

Changxing Miao, Guixiang Xu, Lifeng Zhao

We consider the focusing energy-critical nonlinear Schrödinger equation of fourth order $i u_{t} + Δ^{2} u = ∣ u ∣^{\frac{8}{d - 4}} u$ . We prove that if a maximal-lifespan radial solution $u: I\t…

math.AP2008★ 31 cited

Global well-posedness and scattering for the defocusing $H^{\frac{1}{2}}$ -subcritical Hartree equation in $R^{d}$

Changxing Miao, Guixiang Xu, Lifeng Zhao

We prove the global well-posedness and scattering for the defocusing $H^{\frac{1}{2}}$ -subcritical (that is, $2 < γ < 3$ ) Hartree equation with low regularity data in $R^{d}$ , $d\ge…

math.AP2008★ 47 cited

Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case

Changxing Miao, Guixiang Xu, Lifeng Zhao

We establish global existence, scattering for radial solutions to the energy-critical focusing Hartree equation with energy and $H ˙^{1}$ norm less than those of the ground state…

math.AP2008★ 79 cited

Global well-posedness and scattering for the mass-critical Hartree equation with radial data

Changxing Miao, Guixiang Xu, Lifeng Zhao

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Hartree equation $i u_{t} + Δ u = \pm (∣ x ∣^{- 2} * ∣ u ∣^{2}) u$ for large spherically symmetric $L^2_…

math.AP2007★ 84 cited

Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data

Changxing Miao, Guixiang Xu, Lifeng Zhao

We consider the defocusing, $H ˙^{1}$ -critical Hartree equation for the radial data in all dimensions $(n \geq 5)$ . We show the global well-posedness and scattering results in the…