On the focusing generalized Hartree equation
2020 ◽
Vol 9999
(9999)
◽
pp. 1-20
Keyword(s):
Blow Up
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In this paper we give a review of the recent progress on the focusing generalized Hartree equation, which is a nonlinear Schrodinger-type equation with the nonlocal nonlinearity, expressed as a convolution with the Riesz potential. We describe the local well-posedness in H1 and Hs settings, discuss the extension to the global existence and scattering, or finite time blow-up. We point out different techniques used to obtain the above results, and then show the numerical investigations of the stable blow-up in the L2 -critical setting. We finish by showing known analytical results about the stable blow-up dynamics in the L2 -critical setting.
2017 ◽
Vol 8
(4)
◽
pp. 629-660
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2019 ◽
Vol 26
(2)
◽
pp. 265-288
2019 ◽
Vol 478
(2)
◽
pp. 393-420
◽
1994 ◽
Vol 37
(1)
◽
pp. 101-118
◽
Keyword(s):