好色视频 学术报告[2025]054号

(高水平大学建设系列报告1076号)

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6月22日上午10:30-11:30

报告地点：汇星楼4号教室

报告内容：In this paper, we are concerned with 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 $.

报告人简介：洪广益，华南理工大学副教授，主要从事非线性偏微分方程理论及其应用研究，研究成果发表在Math. Ann.，Indiana Univ. Math. J.，JMPA, SIAM, J. Math. Anal, M3AS, Proc. London Math. Soc，JDE， Nonlinearity等国内外知名期刊上。

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好色视频

2025年6月22日