Asymptotic Stability of the Phase-homogeneous Solution to the Kuramoto-Sakaguchi Equation with Inertia
Asymptotic Stability of the Phase-homogeneous Solution to the Kuramoto-Sakaguchi Equation with Inertia
复制标题
DOI：
10.1137/20m1368719
复制
发表时间：
2018-06
期刊：
影响因子：
--
通讯作者：
Young-Pil Choi;Seung‐Yeal Ha;Qinghua Xiao;Yinglong J. Zhang
中科院分区：
文献类型：
--
作者：
Young-Pil Choi;Seung‐Yeal Ha;Qinghua Xiao;Yinglong J. Zhang
We present the global-in-time existence of strong solutions and its large-time behavior for the Kuramoto-Sakaguchi equation with inertia. The equation describes the evolution of the probability density function for a large ensemble of Kuramoto oscillators under the effects of inertia and stochastic noises. We consider a perturbative framework around the equilibrium, which is a Maxwellian type, and use the classical energy method together with our careful analysis on the macro-micro decomposition. We establish the global-in-time existence and uniqueness of strong solutions when the initial data are sufficiently regular, not necessarily close to the equilibrium, and the noise strength is also large enough. For the large-time behavior, we show the exponential decay of solutions towards the equilibrium under the same assumptions as those for the global regularity of solutions.
