报告人：肖清华（中国科学院武汉物理与数学研究所）

报告题目：Asymptotic stability of the phase-homogeneous solution to the Kuramoto-Sakaguchi equation with inertia

报告摘要：In this talk, we study 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 the perturbation 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 {\color{red}{are}} regular, not necessarily close to the equilibrium, and the noise strength is strong enough. For the large-time behavior, we show the exponential decay rate of solutions towards the equilibrium under same assumptions with that for the global regularity of solutions.

报告人简介：中国科学院武汉物理与数学研究所副研究员，在武汉大学获学士、硕士、博士学位，2012年博士毕业后在韩国首尔国立大学做博士后，2015年至今为武汉物理与数学研究所副研究员，主要从事Boltzmann方程、与Cucker-Smale模型、Kuramoto模型相关动理学方程、双曲守恒律等方面的研究，目前在 Journal of Functional Analysis，SIAM Journal on Mathematical Analysis 等国际期刊发表论文20余篇，主持国家自然科学基金青年基金项目和面上项目各一项。

报告时间：2019年3月7日下午16:00-17:00

报告地点：科技楼南702