Geodesic
On the blow-up phenomenon for the mass-critical focusing Hartree equation in $\mathbb{R}^4$
Changxing Miao1 ; Guixiang Xu1 ; Lifeng Zhao2
1 Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing, China, 100088
2 Department of Mathematics University of Science and Technology of China
Colloquium Mathematicum, Tome 119 (2010) no. 1, pp. 23-50.

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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 analyze the mass concentration phenomenon of such blow-up solutions.
DOI : 10.4064/cm119-1-2
Keywords: characterize dynamics finite time blow up solutions minimal mass focusing mass critical hartree equation mathbb mathbb where make refined gagliardo nirenberg inequality convolution type profile decomposition moreover analyze mass concentration phenomenon blow up solutions

Changxing Miao 1 ; Guixiang Xu 1 ; Lifeng Zhao 2

1 Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing, China, 100088
2 Department of Mathematics University of Science and Technology of China 
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Changxing Miao; Guixiang Xu; Lifeng Zhao. On the blow-up phenomenon for the mass-critical 
focusing Hartree  equation in $\mathbb{R}^4$. Colloquium Mathematicum, Tome 119 (2010) no. 1, pp. 23-50. doi : 10.4064/cm119-1-2. http://geodesic.mathdoc.fr/articles/10.4064/cm119-1-2/

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