Scattering for the focusing Ḣ-critical Hartree equation with radial data
نویسندگان
چکیده
We investigate the focusing Ḣ-critical nonlinear Schrödinger equation (NLS) of Hartree type i∂tu + ∆u = −(| · |−3 ∗ |u|2)u with Ḣ radial data in dimension d = 5. It is proved that if the maximal life-span solution obeys supt ∥|∇| 12 u ∥∥ 2 < √ 6 3 ∥|∇| 12Q ∥∥ 2 , where Q is the positive radial solution to the elliptic equation with nonlocal operator (1.4) which corresponds to a new variational structure. Then the solution is global and scatters.
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تاریخ انتشار 2009