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- W2093702963 abstract "We investigate the focusing nonlinear Schrödinger equation (NLS) of Hartree type i∂tu+Δu=−(|⋅|2−d∗|u|2)u in R5 with initial data in energy space H1. If M[u0]E[u0]<M[Q]E[Q], ‖u0‖2‖∇u0‖2<‖Q‖2‖∇Q‖2. Then the solution with initial data u0 is global and scatters. Here Q is the ground state solution. Moreover, we show that if M[u0]E[u0]<M[Q]E[Q], but ‖u0‖2‖∇u0‖2>‖Q‖2‖∇Q‖2, then the corresponding solution will blow up in finite time. The argument of this work is based on the linear profile decomposition, in the spirit of Kenig–Merle." @default.
- W2093702963 created "2016-06-24" @default.
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- W2093702963 date "2010-08-01" @default.
- W2093702963 modified "2023-10-16" @default.
- W2093702963 title "Scattering for the focusing -critical Hartree equation in energy space" @default.
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- W2093702963 doi "https://doi.org/10.1016/j.na.2010.04.033" @default.
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