报告题目：Stability and decay rates for the 3D compressible Navier-Stokes equations with eddy diffusion

报告人：洪广益副教授（华南理工大学）

报告时间：2025年10月14日下午14:30

报告地点：广东工业大学龙洞校区行政楼610

摘要：In this talk, I will introduce our recent results on the Cauchy problem of the 3D compressible Navier-Stokes equations with eddy diffusion which is commonly used in the study of geophysical flows (cf. Jabin-Bresch, Ann. of Math. 2018). The prominent character of the model is the lack of vertical dissipation of the velocity field. The nonlinear asymptotic stability of the constant equilibrium state with strictly positive constant density and vanishing velocity is established under suitable small initial perturbation in regular Sobolev spaces. Specifically, we show the convergence of the density and velocity towards the corresponding equilibrium state in $H^2(\mathbb{R}^3)$ with almost optimal decay rates. The proof is based on the detailed analysis of the Green function, the time-weighted energy estimates, and the intrinsic coupling structure of the $ \mathop{\mathrm{div}}\nolimits \mathbf{u} $ and $ \nabla \rho $.

个人简介：洪广益，博士，华南理工大学副教授。洪广益博士多年来主要从事非线性偏微分方程的理论及其应用研究，在Math. Ann.、J. Math. Pures Appl.、J. Lond. Math. Soc.、SIAM J. Math. Anal.、Indiana Univ. Math. J.、Math. Models Methods Appl. Sci.、J. Differential Equations、中国科学等国内外知名期刊上发表学术论文十余篇，主持国家自然科学基金项目和广东省自然科学基金项目多项。