姓名 潘星宏
工作单位 南京航空航天大学
摘要 In this talk, we discuss the regularity and Liouville theorems of the axially symmetric (AS) Navier-Stokes (NS) equations. For the non-stationary case, some blow-up criteria and a priori estimates will be given. Besides, A result on “finite speed ASNS passing a cone will be introduced. For the stationary NS equations, some decay rates and a priori assumptions for proving vanishing results of D-solutions will be presented. We will see that there are still gaps to prove Liouville theorems of D-solutions in the whole space R^3 without extra assumptions. However, we can show Liouville theorems of D-solutions in some special unbounded domain such as in a slab and in a cylinder.
简介
潘星宏，副研究员。2017年于南京大学数学系取得理学博士学位。同年入职南京航空航天大学，现为南航副研究员，入选2018年江苏省“双创博士”人才计划。主持江苏省自然科学基金青年基金和国家自然科学基金，参与国家自然科学基金重点项目一项。主要研究方向为Navier-Stokes方程解的正则性和唯一性问题，。目前，在 Arch. Ration. Mech. Anal.，J. Funct. Anal., J. Differential Equations, Calc. Var. Partial Differential Equations, Commun. Contemp. Math.,等杂志发表多篇论文
邀请人：王云