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More precisely, we show that all scaling parameters are necessarily of order $t^{-2}$, and that the corresponding renormalized modulation vector converges to a connected component of a finite-dimensional algebraic set determined by the limiting spatial configuration of the bubbles. This algebraic system encodes the strong interactions between the polynomial tails of the bubbles and governs the effective asymptotic dynamics of the multi-bubble regime.
From: Chencheng Zhang [view email]
[v1]
Wed, 27 May 2026 05:35:16 UTC (61 KB)
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