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A new proof of scattering for the 5D radial focusing Hartree equation
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-12-10
Fanfei Meng

We revisit the scattering result below the ground state of Y. Gao and H. Wu [Scattering for the focusing H ˙ 1 2 -critical Hartree equation in energy space. Nonlinear Anal. 2010;73:1043–1056] on the radial focusing energy-subcritical Hartree equation in d = 5, using the method in Dodson and Murphy [A new proof of scattering below the ground state for the 3D radial focusing cubic NLS. preprint, arXiv:1712.09962]. Using the radial Sobolev embedding and a virial-Morawetz type estimate we can exclude the concentration of mass near the origin instead of using the concentration compactness method in Gao and Wu [Scattering for the focusing H ˙ 1 2 -critical Hartree equation in energy space. Nonlinear Anal. 2010;73:1043–1056].



中文翻译:

5D径向聚焦Hartree方程散射的新证明

我们在Y. Gao和H. Wu的基态下重新观察散射结果[聚焦的散射 H ˙ 1个 2 能量空间中的临界Hartree方程。非线性肛门。2010; 73:1043–1056]  ,使用Dodson和Murphy中的方法研究了d = 5时的径向聚焦能量-亚临界Hartree方程[3D径向聚焦立方NLS在基态下的散射的新证明。预印本,arXiv:1712.09962]。使用径向Sobolev嵌入和viral-Morawetz类型估计,我们可以排除原点附近的质量浓度,而不是在Gao和Wu中使用浓度紧实度方法。 H ˙ 1个 2 能量空间中的临界Hartree方程。非线性肛门。2010; 73:1043-1056]。

更新日期:2020-12-11
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