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The global smooth solution of the 3D incompressible Euler and Navier-Stokes equations in spherical coordinates
时间  Datetime
2019-07-29 10:30 — 11:30 
地点  Venue
Middle Lecture Room(703)
报告人  Speaker
Shu Wang (王术)
单位  Affiliation
北京工业大学
邀请人  Host
李从明,谢峰
报告摘要  Abstract

We investigates the globally stabilizing effects of the geometry of the domain and the solution in studying the regularity issue on the three-dimensional incompressible Navier-Stokes and Euler system. We establish the global existence and uniqueness of the smooth solution to the Cauchy problem for the three-dimensional incompressible Navier-Stokes and Euler system, and, also, to the initial boundary value problem for the 3D Navier-Stokes equations, in spherical coordinates for a class of the smooth large initial data. This is the first result on the global existence and uniqueness of the smooth solution to the 3D incompressible Navier-Stokes and  Euler equations in spherical coordinates. The related problems the axisymmetric Navier-Stokes equations are surveyed and some results on the singularity formation and global regularity of an axisymmetric model for the 3D incompressible Euler and Navier-Stokes equations 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,   “Arch Rational Mech. Anal.”, 212(2014):683-706. See Digital Object Identifier(DOI)10.1007/s00205-013-0716-6.

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.

5. Wang Shu(王术), Wang Yongxin, The existence and uniqueness of global smooth solutions to the 3D incompressible Navier-Stokes and&