数学科学学院学术报告[2023] 101号

(高水平大学建设系列报告873号)

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

报告人：王勇 副研究员（中科院数学与系统科学研究院）

报告时间：2023年12月21日下午2：00-2：50

讲座地点：汇星楼514

报告内容：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 formulatedproblem 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.

报告人简介：王勇，中科院数学与系统科学研究院副研究员，2012年博士毕业于中科院数学与系统科学研究院， 2020年获国家优秀青年科学基金资助，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，在Communications on Pure and Applied Mathematics、Advances in Mathematics 、Archive Rational Mechanics Analysis 和 SIAM Journal in Mathematics Analysis 等国际著名刊物上发表学术论文30余篇。

欢迎师生参加！

邀请人：李杏

数学科学学院

2023年12月18日