The study proves blow up versus global existence in the nonlinear hartree equation, highlighting impacts of kato potential.
In this paper, we study the dynamics of the focusing nonlinear Hartree equation with a Kato potential under some assumptions on the potential . We prove the blow up versus global existence dichotomy for solutions beyond the threshold, based on the method from Duyckaerts–Roudenko in [6]. Our result extends the work of [13], which studied the blow up and scattering theory for solutions of below that threshold.
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Ji et al. (2025) studied this question.
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