Sharp decay rates for localized perturbations to the critical front in the Ginzburg-Landau equation

Autor:	Avery, Montie, Scheel, Arnd
Rok vydání:	2021
Předmět:	Mathematics - Analysis of PDEs Mathematics - Dynamical Systems Nonlinear Sciences - Pattern Formation and Solitons
Druh dokumentu:	Working Paper
Popis:	We revisit the nonlinear stability of the critical invasion front in the Ginzburg-Landau equation. Our main result shows that the amplitude of localized perturbations decays with rate $t^{-3/2}$, while the phase decays diffusively. We thereby refine earlier work of Bricmont and Kupiainen as well as Eckmann and Wayne, who separately established nonlinear stability but with slower decay rates. On a technical level, we rely on sharp linear estimates obtained through analysis of the resolvent near the essential spectrum via a far-field/core decomposition which is well suited to accurately describing the dynamics of separate neutrally stable modes arising from far-field behavior on the left and right. Comment: 37 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2103.10458 Zobrazit plný text záznamu View this record from Arxiv