We consider weak solutions of the Novikov equation that lie in the energy space \(H^1\) with non-negative momentum densities. We prove that a special family of such weak solutions, namely the peakons, is \(H^1\)-asymptotically stable. Such a result is based on a rigidity property of the Novikov solutions which are \(H^1\)-localized and the corresponding momentum densities are localized to the right, which extends the earlier work of Molinet (Arch Ration Mech Anal 230:185–230, 2018; Nonlinear Anal Real World Appl 50:675–705, 2019) for the Camassa–Holm and Degasperis–Procesi peakons. The main new ingredients in our proof consist of exploring the uniform in time exponential decay property of the solutions from the localization of the \(H^1\) energy and redesigning the localization of the total mass from the finite speed of propagation property of the momentum densities.

我们考虑位于非负动量密度的能量空间\（H ^ 1 \）中的Novikov方程的弱解。我们证明了这类弱解的一个特殊族，即波峰，是（H ^ 1 \）-渐近稳定的。这样的结果是基于Novikov解的刚度属性（\（H ^ 1 \）局部化，并且相应的动量密度局部化在右侧），这扩展了Molinet的早期工作（Arch Ration Mech Anal 230：185 – 230，2018;非线性肛门现实世界Appl 50：675–705，2019），用于Camassa–Holm和Degasperis–Procesi峰。我们证明中的主要新成分包括从\（H ^ 1 \）的局部中探索溶液的时间指数衰减性质的均匀性。 能量并根据动量密度的有限传播速度重新设计总质量的局部化。