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Global Solutions of the Compressible Euler-Poisson Equations with Large Initial Data of Spherical Symmetry by Chen, Gui-Qiang G.; He, Lin; Wang, Yong; Yuan, Difan is a scholarly article available to read on EtoBox.

What is Global Solutions of the Compressible Euler-Poisson Equations with Large Initial Data of Spherical Symmetry about?

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 ({\it 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 ({\it i.e.}, concentration) in space-time i

Author

Chen, Gui-Qiang G.; He, Lin; Wang, Yong; Yuan, Difan

Published

2021

Language

EN