演讲人: 王术 教授

讲座时间: 2014.6.11（周三）， 16:00-17:00

讲座地点: 信息楼三层0343会议室

讲座内容:

报告内容:

We study the singularity formation and global regularity of an axisymmetric model for the 3D incompressible Euler and Navier-Stokes equations. This 3D model is derived from the axisymmetric Navier-Stokes equations with swirl using a set of new variables. The model preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected. If we add the convection term back to our model, we would recover the full Navier-Stokes equations. We prove rigorously that the 3D model develops finite time singularities for a large class of initial data with finite energy and appropriate boundary conditions. Moreover, we also prove that the 3D inviscid model has globally smooth solutions for a class of large smooth initial data with some appropriate boundary condition. The related problems are surveyed and some recent results will also be reviewed.

References

1．Hou, Thomas Y.; Li, Congming; Shi, Zuoqiang; Wang, Shu（王术）; Yu, Xinwei. On singularity formation of a nonlinear nonlocal system. Arch. Ration. Mech. Anal. 199 (2011), no. 1, 117–144.

2. Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu（王术） On singularity formation of a 3D model for incompressible Navier-Stokes equations. Adv. Math. 230 (2012), no. 2,607–641.

3. Hou, Thomas Y., Lei, Z., Luo, G., Wang, Shu, Zou, C. On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations, To appear in “Arch Rational Mech. Anal.”, 2013. See Digital Object Identifier(DOI)10.1007/s00205-013-0716-6, 2014.

4. Wang, Shu（王术） On a new 3D model for incompressible Euler and Navier-Stokes equations. Acta Mathematica Scientia.30B(6)(2010): 2089-2102.

演讲人简介:

王术，北京工业大学应用数理学院院长，教授，博士生导师。主要从事物理、力学及交叉学科中的非线性发展偏微分方程方向的研究。

欢迎全体师生参加本次讲座！