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arXiv · 0708.2614

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

Changxing Miao·Guixiang Xu·Lifeng Zhao
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Abstract

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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Changxing Miao, Guixiang Xu, Lifeng Zhao. 2008-08-27. On the blow up phenomenon for the $L^2$-critical focusing Hartree equation in $\Bbb R^4$. https://doi.org/10.4064/cm119-1-2

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