论文标题
Novikov方程的Peamons的渐近稳定性
Asymptotic stability of peakons for the Novikov equation
论文作者
论文摘要
Novikov方程是具有立方非线性的Camassa-Holm型方程。本文旨在证明在$ h^1（\ mathbb {r}）$ - 扰动下的渐近溶液的渐近稳定性满足其相关的动量密度可以定义非阴性ra的尺寸。在Molinet的工作中，我们将首先证明$ h^1（\ Mathbb {r}）$属于某些几乎局部功能的全球解决方案。更确切地说，我们表明这样的解决方案必须是Pearceon。与Camassa-Holm案例相比，我们的分析中的主要困难来自以下事实：动量不是保守的，并且可能沿着轨迹不受限制。另外，为了证明liouville属性，我们使用了与方程式（不保守的）动量无关的新Lyapunov功能。
The Novikov equation is a Camassa-Holm type equation with cubic nonlinearity. This paper aims to prove the asymptotic stability of peakons solutions under $H^1(\mathbb{R})$-perturbations satisfying that their associated momentum density defines a non-negative Radon measure. Motivated by Molinet's work, we shall first prove a Liouville property for $H^1(\mathbb{R})$ global solutions belonging to a certain class of almost localized functions. More precisely, we show that such solutions have to be a peakon. The main difficulty in our analysis in comparison to the Camassa-Holm case comes from the fact that the momentum is not conserved and may be unbounded along the trajectory. Also, to prove the Liouville property, we used a new Lyapunov functional not related to the (not conserved) momentum of the equation.
