On the blow-up phenomenon for the mass-critical focusing Hartree equation in $\mathbb{R}^4$

Tom 119 / 2010

Changxing Miao, Guixiang Xu, Lifeng Zhao Colloquium Mathematicum 119 (2010), 23-50 MSC: 35Q40, 35Q55, 47J35. DOI: 10.4064/cm119-1-2

Streszczenie

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.

Autorzy

  • Changxing MiaoInstitute of Applied Physics and
    Computational Mathematics
    P.O. Box 8009
    Beijing, China, 100088
    e-mail
  • Guixiang XuInstitute of Applied Physics and
    Computational Mathematics
    P.O. Box 8009
    Beijing, China, 100088
    e-mail
  • Lifeng ZhaoDepartment of Mathematics
    University of Science and Technology of China
    e-mail

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