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Analysis reveals asymptotic stability in self-similar blowup behaviors of mass-supercritical NLS dynamics, emphasizing linear stability.
We consider self-similar blowup for (NLS) i∂ t u+Δu+u|u| p-1 =0 in d≥1, focusing on the slightly mass-supercritical range 0<s c :=d 2-2 p-1≪1. The existence and stability of such dynamics [39] and construction of suitable profiles [1] lead to the question of asymptotic stability. In this note, we review the background and recent results [25, 26, 27] on the asymptotic stability, with particular emphasis on mode stability and linear stability.
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Zexing Li (2025) studied this question.
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