报告题目

Decay estimates for anisotropic Navier-Stokes equations andBoussinesq equations

报告摘要

In this talk, we report the decay estimates on anisotropic Navier-Stokes equations in the 3D half-space.By introducing suitable Chemin-Lerner type spaces, we obtain the optimal decay estimates of global small solutions in the Lebesgue space. In particular, we reveal the enhanced dissipation mechanism of the third component of velocity field. More precisely, we show that the horizontal components decay as the 2D heat kernel, while the vertical component decays as the 3D heat kernel.Foranisotropic Boussinesq equations, we show that not only the enhanced dissipation mechanism, but also the dispersive effect happens.

个人简介

李扬，安徽大学数学科学学院副教授，2019年12月博士毕业于南京大学，导师为孙永忠教授。研究领域为流体力学中的偏微分方程。主持国家自然科学基金青年项目、面上项目与安徽省自然科学基金面上项目，在Int. Math. Res. Not., SIAM J.Numer.Anal., Calc. Var. Partial Differential Equations, SIAM J.Math.Anal., IMAJ.Numer.Anal., Nonlinearity, J.Differential.Equations.等期刊发表论文约20篇。

报告时间：2025年12月13日（周六）上午10：00--11：00

报告地点：知新楼B座924

邀请人： 陶涛 数学学院教授