报告人：张挺教授

浙江大学

题目：Some wellposedness results for 3D axisymmetric Navier-Stokes system

时间：2018年5月11日上午10:15

地点：海韵实验楼105

摘要：In this talk, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair $(\frac{\omega^{r}}{r},\frac{\omega^{\theta}}{r})$, we get several Prodi-Serrin type regularity criteria based on the angular velocity, $u^\theta$. Moreover, we obtain the global well-posedness result if the initial angular velocity $u_{0}^{\theta}$ is appropriate small in the critical space $L^{3}(\R^{3})$. Furthermore, we investigate the global well-posedness for the 3-D inhomogeneous incompressible Navier-Stokes system with the axisymmetric initial data. We prove the global well-posedness provided that $\|\frac{a_{0}}{r}\|_{\infty}$ and $\|u_{0}^{\theta}\|_{3}$ are sufficiently small, and obtain some decay estimates. At last, considering  the stochastic three-dimensional  Navier-Stokes system with the axisymmetric initial data and white noise, we prove that the axisymmetric pathwise solution is global in probability under the condition that the swirl component of the initial velocity field $u_0^\theta$ and the white noise $\sigma^\theta$ are sufficiently small. Furthermore, the pathwise axisymmetric solution is global almost surely in the no swirl case. (Based on joint works with Hui Chen, Lihuai Du, Daoyuan Fang)..

报告人简介：张挺，博士、浙江大学教授。2001年、2006年于浙江大学获学士、博士学位。获首批青年拔尖人才支持计划（2012年）、浙江省“新世纪151人才工程”第二层次培养人员、教育部新世纪优秀人才支持计划（2011年）、全国优秀博士学位论文提名论文奖（2008年）等。张挺教授的研究方向为偏微分方程；论文发表在Arch. Rational. Mech. Anal.、Comm. Math. Phys.、J. Math. Pures Appl.等，与方道元教授合作出版专著1本。.

联系人:王焰金教授

欢迎广大师生参加！