【10月18日】How far p≈=v^2 in the regularity theory of the Navier-Stokes equations?

2018-10-08

时间:2018.10.18

地点:理学院楼331报告厅

申办单位:理学院

主讲人:Hugo Beirao da Veiga

国籍:意大利

使用语言:英文

主讲人简介:

Hugo Beirao da Veiga, 现为意大利比萨大学数学系教授,  1971 年获法国巴黎六大博士学位,师从G. Stampacchia 教授。 从事偏微分方程、泛函分析及数学流体力学理论的研究, 尤其是在Navier-Stokes 方程等流体力学方程的研究方面有诸多杰出的工作。在CPAM、JEMS、 JMPA、ARMA  等国际著名期刊上发表130多篇学术论文,是多家国际期刊的编委。

内容摘要:

The starting point of this talk is the well known sufficient condition for regularity of weak solutions to the evolution Navier-Stokes equations, sometimes called Prodi-Serrin's condition (PS condition). Roughly speaking, it establishes that solutions v which belong to the functional space L^r(O,T;L^q(Ω)), where 2/r +n/q =1 and q>n , are regular. On the other hand, a formal equivalence p≈=|v|^2 is suggested by the well known equation 

In three papers published nearly twenty years ago we have proved some results which support this equivalence. In a recent paper we obtained new results in this direction. Interesting open problems still remain.