含真空的可壓縮流體N-S方程到Euler方程的粘性消失極限

發布者:文明辦發布時間:2019-06-10瀏覽次數:245


主講人:李亞純 上海交通大學數學科學學院教授 博士生導師


時間:2019年6月13日10:00


地點:徐匯校區3號樓332報告廳


舉辦單位:數理學院


主講人介紹:李亞純,上海交通大學數學科學學院教授,博士生導師。長期從事非線性偏微分方程的理論與應用研究,近年來在流體力學方程組的數學理論研究方面發表相關論文40余篇,并有多篇論文被收錄在專著或系列叢書中,出版英文譯著兩本。先后主持了國家自然科學基金項目十余項(包括重點項目一項),上海市自然科學基金項目兩項。入選上海市曙光人才計劃、教育部新世紀優秀人才計劃等項目,與同事合作獲得上海市自然科學一等獎。  


內容介紹:We establish the vanishing viscosity limit of the Navier-Stokes equations to the  Euler equations for three-dimensional compressible isentropic flow in the whole  space. When the viscosity coefficients are given as constant multiples of the  density's power,it is shown that there exists a unique regular solution of  compressible Navier-Stokes equations with arbitrarily large initial data and  vacuum, whose life span is uniformly positive in the vanishing viscosity limit.  Via introducing a ``quasi-symmetric hyperbolic--``degenerate elliptic coupled  structure to control the behavior of the velocity of the fluid near the vacuum,  we establish some uniform estimates which lead the strong convergence of the  regular solution of the viscous flow to that of the inviscid flow, we also give  the rate of convergence. Furthermore, we point out that our framework is also  applicable to other physical dimensions, say 1 and 2, with some minor  modifications. This is a joint work with Yongcai Geng and Shengguo Zhu.

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