报告题目：Local-in-time well-posedness of inhomogeneousanisotropic incompressible Navier-Stokes equations

报告人：高金城

报告时间：2023年10月30日15:00-16:00

报告地点：88038威尼斯323（腾讯会议932 495 5583）

邀请单位：88038威尼斯

报告内容简介：

In the work [H.J. Choe and H. Kim,Commun. Partial Differ. Equ. 28 (5-6) 1183-1201 (2003)],the local-in-time well-posedness theory was established for the inhomogeneousincompressible Navier-Stokes (INS) equations with vacuum under the condition ofinitial data satisfying some compatibility condition.It is worth noting that these INS equations obey full dissipative structure.In this paper, we investigate the local-in-time well-posedness theory for theinhomogeneous INS equations with vacuum and only horizontaldissipative structure.Due to the lack of the vertical dissipative term and appearance of vacuum,it is a highly challenging tricky problem for us to establish the well-posedness result.To this end, we develop some good estimates for the density and vorticityto control the nonlinear term.Therefore, we find the appropriate function space to establish the local-in-timewell-posedness theory for the inhomogeneous INS equationswith far-field vacuum and only horizontal dissipative structure.

报告人简介：

高金城，中山大学数学学院副教授，主要从事流体力学相关方程的理论与应用研究，在时间衰减估计、适定性和粘性消失极限方程取得了一些好的成果，相关论文发表在Calc. Var. Partial Differential Equations，Ann. Inst. H. Poincaré C Anal. Non Linéaire, Phys. D，J. Differential Equations等杂志上。先后主持和参与了国家重点研发项目、国家自然科学基金青年项目、国家博士后基金项目、广东省基金项目和广州市项目。