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微分方程与动力系统系列报告(2022/6/30 9:30-12:30,报告人:王勇副研究员)

发布人:日期:2022年06月27日 09:06浏览数:

报告时间:20226309:30-12:30

报告地点:腾讯会议号:986-907-056

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

报告摘要:We are concerned with a global existence theory for finite-energy solutions of the multidimensional Euler-Poisson equations for both compressible gaseous stars and plasmas 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. To solve this problem, we develop a new approach for the construction of approximate solutions as the solutions of an appropriately formulated free boundary 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-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.

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,入选中科院数学与系统科学研究院“陈景润未来之星”计划。2020年获国家优秀青年科学基金资助,主要研究非线性双曲守恒律(可压缩Euler方程组)、可压缩Navier-Stokes,、Boltzmann方程等的适定性问题以及相应的流体动力学极限问题。相关研究成果被Commun.Pure Appl.Math, Adv.Math, Arch.Ration.Mech.Anal, Siam J.Math.Anal等国际著名数学刊物接受或发表。



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