报告人 ：吴国春(华侨大学)

日期：2020年10月24日

时间：15:30开始

地址：理科楼LA106

报告摘要：We investigate the large--time behavior of strong solutions to a two-phase fluid model in the whole space $\mathbb R^3$. This model was first derived by Choi [Y. P. Choi: Global classical solutions and large-time behavior of the two-phase fluid model. SIAM J. Math. Anal.] by taking the hydrodynamic limit from the Vlasov-Fokker-Planck/isentropic Navier-Stokes equations with strong local alignment forces. Under the assumption that the initial perturbation around an equilibrium state is sufficiently small, the global well-posedness issue has been established in [Y. P. Choi: Global classical solutions and large-time behavior of the two-phase fluid model. SIAM J. Math. Anal.]. However, as indicated by Choi in [Y. P. Choi: Global classical solutions and large-time behavior of the two-phase fluid model. SIAM J. Math. Anal.], the large-time behavior of these solutions has remained an open problem. In this article, we resolve this problem by proving convergence to its associated equilibrium with the optimal rate which is the same as that of the heat equation. Particularly, the optimal convergence rates of the higher-order spatial derivatives of the solutions are also obtained. Moreover, for well-chosen initial data, we also show the lower bounds on the convergence rates. Our method is based on Hodge decomposition, low-frequency and high-frequency decomposition, delicate spectral analysis and energy methods.

报告人简介：吴国春，华侨大学副教授，博士毕业于厦门大学，中国科学院数学与系统科学研究院博士后。研究方向为偏微分方程。

联系人：穆春来 王华桥

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