On the blow up phenomenon for the $L^2$-critical focusing Hartree equation in $\Bbb R^4$

Changxing Miao; Guixiang Xu; Lifeng Zhao

arxiv: 0708.2614 · v4 · pith:73K5O2FY · submitted 2007-08-20 · math.AP · math-ph· math.MP

On the blow up phenomenon for the L²-critical focusing Hartree equation in Bbb R⁴

Changxing Miao , Guixiang Xu , Lifeng Zhao This is my paper

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We characterize the dynamics of the finite time blow up solutions with minimal mass for the focusing mass critical Hartree equation with $H^1(\mathbb{R}^4)$ data and $L^2(\mathbb{R}^4)$ data, where we make use of the refined Gagliardo-Nirenberg inequality of convolution type and the profile decomposition. Moreover, we also analyze the mass concentration phenomenon of such blow up solutions.

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On the blow up phenomenon for the L²-critical focusing Hartree equation in Bbb R⁴

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