報告題目：Some Recent Results on Compressible Navier-Stokes Equations
報 告 人：李競 研究員 中科院數學與系統科學研究院、南昌大學
報告時間：2022年6月20日 星期一 下午15:30-16:30
報告地點：騰訊會議 ID：619-476-801
點擊鍊接入會，或添加至會議列表：https://meeting.tencent.com/dm/a70q68FjZdys
校内聯系人：王春朋 wangcp@jlu.edu.cn
報告摘要：We investigate the barotropic compressible Navier-Stokes equations with slip boundary conditions in a three-dimensional (3D) simply connected bounded domain, whose smooth boundary has a finite number of two-dimensional connected components. For any adiabatic exponent bigger than one, after obtaining some new estimates on boundary integrals related to the slip boundary conditions, we prove that both the weak and classical solutions to the initial-boundary-value problem of this system exist globally in time provided the initial energy is suitably small. Moreover, the density has large oscillations and contains vacuum states. Finally, it is also shown that for the classical solutions, the oscillation of the density will grow unboundedly in the long run with an exponential rate provided vacuum appears (even at a point) initially. This is the first result concerning the global existence of classical solutions to the compressible Navier-Stokes equations with density containing vacuum states initially for general 3D bounded smooth domains. This is a joint work with Guocai Cai (Xiamen University).
報告人簡介：李競，中科院數學與系統科學研究院研究員，國家傑出青年基金獲得者，南昌大學特聘教授、博士生導師，現任南昌大學數學與交叉科學研究院院長。2004年8月香港中文大學數學專業博士畢業，2015年獲國家傑出青年科學基金，2018年獲得首屆世界華人數學家聯盟大會(ICCM)五年最佳論文銀獎，入選江西省“雙千計劃”創新領軍人才。主要研究方向為可壓縮Navier-Stokes方程，證明了三維空間可壓縮Navier-Stokes方程含真空的大震蕩古典解的整體存在性等一系列重要結果，研究工作發表在Comm. Pure Appl. Math.、Arch. Ration. Mech. Anal.、Comm. Math. Phys. 等國際著名數學雜志，論文被引用1100餘次。
