On blow-up for the Hartree equation

Volume 126 / 2012

Jiqiang Zheng Colloquium Mathematicum 126 (2012), 111-124 MSC: 35Q40, 35Q55. DOI: 10.4064/cm126-1-8

Abstract

We study the blow-up of solutions to the focusing Hartree equation $iu_t+ \Delta u+(|x|^{-\gamma }*|u|^2)u=0$. We use the strategy derived from the almost finite speed of propagation ideas devised by Bourgain (1999) and virial analysis to deduce that the solution with negative energy ($E(u_0)<0$) blows up in either finite or infinite time. We also show a result similar to one of Holmer and Roudenko (2010) for the Schrödinger equations using techniques from scattering theory.

Authors

  • Jiqiang ZhengThe Graduate School of China Academy of Engineering Physics
    P.O. Box 2101, Beijing, China, 100088
    e-mail

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