Novikov方程中$H^1$稳定顶点的$W^{1，\infty}$不稳定性

IF 1.1 3区数学 Q2 MATHEMATICS, APPLIED

Dynamics of Partial Differential Equations Pub Date : 2019-11-19 DOI:10.4310/dpde.2021.v18.n3.a1

R. Chen, D. Pelinovsky

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引用次数: 6

摘要

从以前的工作中可以知道，Novikov方程的peakon解在$H^1$中是轨道渐近稳定的。我们用特征方法证明了这些peakon解在$W^｛1，\infty｝$扰动下是不稳定的。此外，我们证明了Novikov peakons的小的初始$W^｛1，\infty｝$扰动可以导致相应解的有限时间爆破。

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$W^{1,\infty}$ instability of $H^1$-stable peakons in the Novikov equation

It is known from the previous works that the peakon solutions of the Novikov equation are orbitally and asymptotically stable in $H^1$. We prove, via the method of characteristics, that these peakon solutions are unstable under $W^{1,\infty}$-perturbations. Moreover, we show that small initial $W^{1,\infty}$-perturbations of the Novikov peakons can lead to the finite time blow-up of the corresponding solutions.

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来源期刊

Dynamics of Partial Differential Equations 数学-应用数学

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes novel results in the areas of partial differential equations and dynamical systems in general, with priority given to dynamical system theory or dynamical aspects of partial differential equations.