学术报告

题      目：Global well-posedness of regular solutions to the 3-D isentropic compressible Navier-Stokes Equations with degenerate viscosities and vacuum

报  告  人：朱圣国  副教授  (邀请人：袁源 )

                                    上海交通大学

时      间：4月27日  10：30-11：30

地     点：数科院西楼111报告厅

报告人简介:

        朱圣国，上海交通大学数学科学学院副教授、博导。2015年于上海交通大学获理学博士学位。毕业之后先后在香港中文大学、澳大利亚莫纳什大学、英国牛津大学做博士后。2020年返回上海交大任教。主要从事与流体力学及相对论相关的非线性偏微分方程的理论研究工作，在可压缩Navier-Stokes 及Euler方程组的适定性和奇异性方面取得了系统性的研究进展。目前已在国际学术期刊上发表学术论文30余篇，其中包括Transactions of the AMS、Advances in Mathematics、Arch. Ration. Mech. Anal.、Ann. Inst. H. Poincare Anal. Non Lineaire、J. Math. Pures Appl. 等本领域权威杂志。 并于2017年入选英国皇家学会”Newton International Fellow”;  2019年入选中组部国家海外高层次人才引进计划（青年项目）；2020年入选上海市海外高层次人才引进计划。 目前主持科技部国家重点研发计划青年科学家项目一项。

摘      要：

        We talk about the Cauchy problem for the 3-D isentropic compressible Navier-Stokes equations with degenerate viscosities. By introducing some new variables and making use of the `` quasi-symmetric hyperbolic--``degenerate elliptic coupled structure to control the behavior of the fluid velocity,  we prove the global-in-time well-posedness of regular solutions with vacuum for a class of smooth initial data that are of small density but possibly large velocities. Here the initial mass density is required to decay to zero in the far field, and the spectrum of the Jacobi matrix of the initial velocity are all positive. The result here applies to a class of degenerate density-dependent viscosity coefficients, is independent of the BD-entropy, and seems to be the first on the global existence of smooth solutions which have large velocities and contain vacuum state for such degenerate system in three space dimensions. This talk is based on a joint work with Prof. Zhouping Xin (CUHK).

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