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

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

2007-08-20

arxiv.org/abs/0708.2614v4

Colloquium Mathematicum, 119(2010)23-50

Mathematics

Analysis of PDEs

25pages

Scientific paper

10.4064/cm119-1-2

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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