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Homogeneous Solutions of Stationary Navier–Stokes Equations with Isolated Singularities on the Unit Sphere

编辑:xyx 时间:2018年07月26日 访问次数:290

浙江大学数学科学学院九十周年院庆系列活动之六十二

题目: Homogeneous Solutions of Stationary Navier–Stokes Equations with Isolated Singularities on the Unit Sphere
报告人:李岩岩教授(美国 Rutgers 大学)
时间:2018年7月30日(周一)上午10:00-12:30
地点:浙江大学玉泉校区逸夫工商楼4楼报告厅
摘要:
We classify all (−1)-homogeneous axisymmetric no-swirl solutions of incom- pressible stationary Navier–Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, and analyze their pressure profiles near the north pole. Then we prove that there is a curve of (−1)-homogeneous axisymmetric solutions with nonzero swirl, having the same smoothness property, emanating from every point of the interior and one part of the boundary of the solution surface. Moreover we prove that there is no such curve of solutions for any point on the other part of the boundary. We also establish asymptotic expansions for every (−1)-homogeneous axisymmetric solutions in a neighborhood of the singular point on the unit sphere.   This is a joint work with Li Li and Xukai Yan.
主讲人简介:
李岩岩教授, 现任Rutgers大学数学系杰出教授,非线性分析研究中心主任,北京师范大学客座教授。李岩岩教授本科毕业于中国科学技术大学,中国科学院硕士毕业后,在纽约大学克朗所获得博士学位,师从著名的分析数学家Louis Nirenberg。主要从事偏微分方程、几何分析等方向的研究。李教授是2012年美国数学会会士(Inaugural Class of Fellows);国际数学家大会45分钟报告人;斯隆科研奖获得者。李岩岩教授是偏微分方程,非线性分析领域非常活跃的专家,迄今为止发表了超过130篇SCI论文,担任多个国际杂志的主编或编委。

联系人: 张挺(zhangting79@zju.edu.cn )   
 
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Title: Homogeneous Solutions of Stationary Navier–Stokes Equations with Isolated Singularities on the Unit Sphere
Speaker: Prof. Yanyan Li (Rutgers University)
Time: July 30, 2018, 10:00-12:30
Place: Sir Run Run Shaw Building 4th floor
Abstract:
We classify all (−1)-homogeneous axisymmetric no-swirl solutions of incom- pressible stationary Navier–Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, and analyze their pressure profiles near the north pole. Then we prove that there is a curve of (−1)-homogeneous axisymmetric solutions with nonzero swirl, having the same smoothness property, emanating from every point of the interior and one part of the boundary of the solution surface. Moreover we prove that there is no such curve of solutions for any point on the other part of the boundary. We also establish asymptotic expansions for every (−1)-homogeneous axisymmetric solutions in a neighborhood of the singular point on the unit sphere.   This is a joint work with Li Li and Xukai Yan.
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