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发表时间:2021-03-08 阅读次数:31次
报告题目: Regularity for the Navier-Stokes Equations via Liouville Type Theorems(1)
报 告 人:Professor Grigory Seregin
报告人所在单位:University of Oxford, UK
报告日期:2021-03-08 星期一
报告时间:16:30 – 17:30
报告地点:ZOOM Meeting ID: 876 1464 0705,Passcode: 753770
  
报告摘要:

We are going to discuss how Liouville-type theorems for the

Navier-Stokes equations are related with the local regularity theory of weak

solutions to those equations. The notion of mild bounded ancient solutions

and even more general local energy ancient solutions are going to be introduced

and discussed. The conjecture about the relationship between potential

Type I blowups of solutions to the Navier-Stokes equations and Liouville type

theorems for ancient solutions will be explained. We also going to prove

Liouville-type theorems in a few cases like 2D-case, case with axial symmetry, and so on.In particular, we will show that there is no Type I blowups foraxisymmetric conditions.

 

The Liouville-type theorem for steady-state so-called D-solutions to the

Navier-Stokes equations will be discussed in connections with the problem

of uniqueness of solutions describing the flow past an obstacle. Although the

Liouville type theorem has not been solved in the full generality, we shall

consider a few interesting particular cases.

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