报告人：洪广益 副教授 (华南理工大学)

时间：2025年03月15日 10:00-

地点：理科楼LA103

摘要：In this talk, 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 $H^2$ 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 $.

邀请人: 王华侨

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