报告题目 Liouville type theorems for steady Navier-Stokes equations
报 告 人： 王 云 教授
工作单位： 苏州大学
报告时间： 2022-11-14(周一) 8:30-11:30
腾讯会议ID： 794 364 7383
报告摘要：
In this talk, we will discuss some Liouville-type theorems for the steady incompressible Navier-Stokes system in a slab. When the no-slip boundary conditions are prescribed, we prove that any bounded solution is trivial if it is axisymmetric or ru^r is bounded, and that general three-dimensional solutions must be Poiseuille flows when the velocity is not big in L∞ space. When the periodic boundary conditions are imposed on the slab boundaries, we prove that the bounded solutions must be constant vectors if the swirl velocity or the radial velocity is independent of the angular variable, or ru^r decays to zero. The proofs are elementary and are based on energy estimates. The key technique is to establish a Saint-Venant type theorem that characterizes the growth of Dirichlet integral of nontrivial solutions. This is a joint work with J. Bang, Changfeng Gui, and Chunjing Xie.
报告人简介：
王云，苏州大学教授，博士毕业于香港中文大学。主要研究领域为不可压缩流的适定性问题，特别是非齐次不可压方程与管道流问题。曾多次主持国家自然科学基金项目。
