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This is a Quantitative Study study.

October 13, 2025

The dynamics of the focusing NLH with a potential beyond the mass–energy threshold

Key Points

The study establishes a blow up versus global existence dichotomy in solutions beyond the threshold.
Key findings indicate that under certain conditions, solutions may either blow up or exist globally depending on the potential.
Analysis employs the method from Duyckaerts–Roudenko, building on previous work in the field.
Extends prior research on scattering theory and dynamics below the mass-energy threshold in nonlinear equations.

Abstract

Abstract 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.

The dynamics of the focusing NLH with a potential beyond the mass–energy threshold

Key Points

Abstract

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