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- W2116721163 abstract "We consider the focusing energy-critical nonlinear Hartree equation iut+Δu=−(|x|−4∗|u|2)u. We proved that if a maximal-lifespan solution u:I×Rd→C satisfies supt∈I‖∇u(t)‖2<‖∇W‖2, where W is the static solution of the equation, then the maximal-lifespan I=R, moreover, the solution scatters in both time directions. For spherically symmetric initial data, similar result has been obtained in [C. Miao, G. Xu, L. Zhao, Global wellposedness, scattering and blowup for the energy-critical, focusing Hartree equation in the radial case, Colloq. Math., in press]. The argument is an adaptation of the recent work of R. Killip and M. Visan [R. Killip, M. Visan, The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher, preprint] on energy-critical nonlinear Schrödinger equations." @default.
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- W2116721163 date "2009-02-01" @default.
- W2116721163 modified "2023-10-06" @default.
- W2116721163 title "The focusing energy-critical Hartree equation" @default.
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- W2116721163 doi "https://doi.org/10.1016/j.jde.2008.05.013" @default.
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