Geodesic
On blow-up for the Hartree equation
Jiqiang Zheng1
1 The Graduate School of China Academy of Engineering Physics P.O. Box 2101, Beijing, China, 100088
Colloquium Mathematicum, Tome 126 (2012) no. 1, pp. 111-124 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm126-1-8
Keywords: study blow up solutions focusing hartree equation delta gamma * strategy derived almost finite speed propagation ideas devised bourgain virial analysis deduce solution negative energy blows either finite infinite time result similar holmer roudenko schr dinger equations using techniques scattering theory

Jiqiang Zheng 1

1 The Graduate School of China Academy of Engineering Physics P.O. Box 2101, Beijing, China, 100088 
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Jiqiang Zheng. On blow-up for the Hartree equation. Colloquium Mathematicum, Tome 126 (2012) no. 1, pp. 111-124. doi: 10.4064/cm126-1-8

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