On blow-up for the Hartree equation

• Autorzy: Jiqiang Zheng
• Języki publikacji: EN

Abstrakty

EN

We study the blow-up of solutions to the focusing Hartree equation $iu_{t} + Δu + (|x|^{-γ}*|u|²)u = 0$. 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(u₀) < 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.

Kategorie tematyczne

• 35Q55: NLS-like equations (nonlinear Schr\"odinger)
• 35Q40: PDEs in connection with quantum mechanics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 126
• Numer: 1
• Strony: 111-124

Daty

wydano

2012

Twórcy

autor

Jiqiang Zheng

• The Graduate School of China Academy of Engineering Physics, P.O. Box 2101, Beijing, China, 100088

Identyfikatory

DOI

10.4064/cm126-1-8