On the blow-up phenomenon for the mass-critical focusing Hartree equation in $\mathbb{R}^4$
Volume 119 / 2010
Colloquium Mathematicum 119 (2010), 23-50
MSC: 35Q40, 35Q55, 47J35.
DOI: 10.4064/cm119-1-2
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 analyze the mass concentration phenomenon of such blow-up solutions.
