報告題目：On regular solutions for three-dimensional full compressible Navier-Stokes equations with degenerate viscosities and far field vacuum

報告人：  朱聖國教授（上海交通大學）

報告時間：2024年4月13日星期六10:00-11:00

會議地點：勵學樓B110

邀請人：  程 星

報告摘要：The Cauchy problem for the 3-D full degenerate compressible Navier-Stokes equations with far field vacuum is considered. First, when shear and bulk viscosity coefficients both depend on the absolute temperature in a power law of Chapman-Enskog, based on some elaborate analysis of this system’s intrinsic singular structures, we identify one class of initial data admitting a local-in-time regular solution with far field vacuum in terms of the mass density, velocity and entropy. Furthermore, it is shown that within its life span of such a regular solution, the velocity stays in an inhomogeneous Sobolev space, the entropy has uniformly finite lower and upper bounds in the whole space, and the laws of conservation of total mass, momentum and total energy are all satisfied. Note that due to the appearance of the vacuum, the momentum equations are degenerate both in the time evolution and viscous stress tensor, and the physical entropy for polytropic gases behaves singularly, which make the study on corresponding well-posedness challenging. For proving the existence, we first introduce an enlarged reformulated structure by considering some new variables, which can transfer the degeneracies of the full CNS to the possible singularities of some special source terms related with the entropy, and then carry out some singularly weighted energy estimates carefully designed for this reformulated system. This talk is based on a joint work with Dr. Qin Duan and Prof. Zhouping Xin.

報告人簡介：朱聖國，男，上海交通大學數學科學學院副教授、博導。2015年于上海交通大學獲理學博士學位。畢業之後先後在香港中文大學、澳大利亞莫納什大學、英國牛津大學做博士後。2020年返回上海交大任教。主要從事與流體力學及相對論相關的非線性偏微分方程的理論研究工作，在可壓縮Navier-Stokes 及Euler方程組的适定性和奇異性方面取得了系統性的研究進展。目前已在國際學術期刊上發表學術論文30餘篇，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. 等本領域權威雜志。 并于2017年入選英國皇家學會”Newton International Fellow”;  2019年入選中組部國家海外高層次人才引進計劃（青年項目）；2020年入選上海市海外高層次人才引進計劃。 目前主持科技部國家重點研發計劃青年科學家項目一項。