题目:Global Solutions of the Compressible Euler and Euler-Poisson Equations with Large Initial Data of Spherical Symmetry

主讲人：王勇

摘要:In this talk, we are concerned with the global existence theory for finite-energy solutions of the multidimensional compressible Euler equations and Euler-Poisson equations (both gaseous stars and plasmas are included) with large initial data of spherical symmetry. One of the main challenges is the strengthening of waves as they move radially inward towards the origin, especially under the self-consistent gravitational field for gaseous stars. A fundamental unsolved problem is whether the density of the global solution forms a delta measure (i.e., concentration) at the origin. We develop a new approach for the construction of approximate solutions as the solutions of an appropriately formulated problem for the compressible Navier-Stokes(-Poisson) equations with a carefully adapted class of degenerate density-dependent viscosity terms, so that a rigorous convergence proof of the approximate solutions to the corresponding global solution of the compressible Euler equations and Euler-Poisson equations with large initial data of spherical symmetry can be obtained. Even though the density may blow up near the origin at a certain time, it is proved that no delta measure (i.e., concentration) in space-time is formed in the vanishing viscosity limit for the finite-energy solutions of the compressible Euler-Poisson equations for both gaseous stars and plasmas in the physical regimes under consideration. The talk is based on joint works with G.Q. Chen, F.M. Huang, T.H. Li, L. He, W.Q. Wang, D.F. Yuan.

个人简介:王勇，2012年博士毕业于中科院数学与系统科学研究院，现任中科院数学与系统科学研究院副研究员，主要研究可压缩Euler方程、可压缩Navier-Stokes方程、Boltzmann方程等方程的适定性和流体动力学极限，曾获得国家自然科学基金委员会优秀青年科学基金的资助。公开发表SCI论文30余篇， 主要学术论文发表在 Comm. Pure Appl. Math., Comm. Math.Phys., Adv. Math., Arch. Ration. Mech. Anal., SIAM J. Math. Anal.等刊物上。

报告时间：2024年3月29日（周五）上午10:30-11:30

地点：中心校区知新楼B924

邀请人：陶涛 副教授