關于舉行香港城市大學楊彤院士學術報告會的通知

發布時間:2020-01-13設置

報告題目:Prandtl Boundary Layer System and Beyond
報 告 人:楊彤 院士(香港城市大學)
報告時間:2020年1月16日(星期四)下午16:00-17:00
報告地點:37號樓3A02室
歡迎廣大師生前往!
 
 
數學學院
2020年1月13日
 
報告摘要:
In 1904, Prandtl introduced a fundamental system derived from the incompressible Navier-Stokes equation with no-slip boundary condition to capture the behavior of fluid motion near the boundary when viscosity vanishes. Even though there are fruitful mathematical theories developed since the seminal works by Oleinik in 1960s, most of the well-posedness theories are limited to the two space dimensions under Oleinik's monotonicity condition except the classical work by Sammartino-Caflisch in 1998 in the framework of analytic functions and some recent work in Gevrey function spaces.
In addition to its early application in aerodynamics and later in various areas in fluid dynamics and engineering, Prandtl equation can be viewed as a typical example of partial differential equations with rich structure that includes mixed type and degeneracy in dissipation. Hence, it provides many challenging mathematical problems and most of them remain unsolved after more than one hundred years from its derivation.
In this talk, we will present the intrinsic structure of the Prandtl operator and it various forms and relation with other physical models.
 
報告人簡介:
楊彤,香港城市大學講席教授(Chair Professor),歐洲科學院院士。目前擔任香港數學會主席(2016-)。主持的科研項目“守恒律組和玻爾茲曼方程的一些數學理論”獲得2012年度國家自然科學獎二等獎;1998年獲得首屆國際華人數學家大會晨興數學獎銀獎;2011年獲得香港裘槎基金會高級研究成就獎(Croucher Senior Research Fellowship 2011/2012)。曾擔任SCI雜志Analysis and Applications (2013-2017)副主編,以及作為SCI雜志Kinetic and Related Models的創刊副主編之一。
楊彤院士長期從事非線性偏微分方程的研究,特別是在雙曲守恒律和玻爾茲曼方程的研究中作出了重要的工作,產生了重大影響。關于雙曲守恒律,楊彤院士與其合作者引入了新的廣義熵泛函——后被稱為“劉-楊泛函”,并建立了一個圓滿的適定性理論,這一新的思路已被同行應用及推廣到其他的數學領域。關于玻爾茲曼方程,楊彤院士與其合作者引入了新的宏觀與微觀分解,建立了玻爾茲曼方程與流體動力學方程的一個直接橋梁,得到了基本波與解的存在性與穩定性等一系列重要結果。
 

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