Global solutions of the compressible Euler‐Poisson equations with large initial data of spherical symmetry
Global solutions of the compressible Euler‐Poisson equations with large initial data of spherical symmetry
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DOI：
10.1002/cpa.22149
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发表时间：
2021-01
影响因子：
3
通讯作者：
Gui-Qiang G. Chen;Lin He;Yong Wang;Difan Yuan
中科院分区：
文献类型：
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作者：
Gui-Qiang G. Chen;Lin He;Yong Wang;Difan Yuan
我们关注的是具有球对称大初始数据的可压缩气态星和等离子体的多维欧拉-泊松方程有限能量解的整体存在性理论。其中一个主要的挑战是波的加强，因为它们径向向内移动到原点，特别是在气体恒星的自洽引力场下。一个基本的未解决问题是全局解的密度是否形成Delta度量（即，浓度）。为了解决这个问题，我们开发了一种新的方法来构造近似解作为可压缩Navier‐Stokes‐Poisson方程的适当形式的自由边界问题的解，该方程具有一类仔细调整的退化密度依赖粘性项，从而严格证明了具有大初始值的可压缩Euler‐Poisson方程的近似解到相应整体解的收敛性。可以获得对称性。即使密度可能在某个时刻在原点附近爆炸，也证明了没有δ测度（即，在考虑的物理制度中，对于气态恒星和等离子体的可压缩欧拉-泊松方程的有限能量解，在消失的粘性极限中形成时空中的浓度（浓度）。
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.