Newtonian limit for the relativistic Euler-Poisson equations with vacuum
Newtonian limit for the relativistic Euler-Poisson equations with vacuum
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DOI：
10.1016/j.jde.2022.01.003
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发表时间：
2022-03
影响因子：
2.4
通讯作者：
La-Su Mai;Ming Mei
中科院分区：
文献类型：
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作者：
La-Su Mai;Ming Mei
本文讨论相对论Euler-Poisson方程的牛顿极限。在自由边界和真空条件下，证明了局部光滑解的存在唯一性，局部光滑解以c−2的速度收敛于经典欧拉-泊松方程的解，其中c为光速.从数学的角度出发，我们成功地克服了洛伦兹因子、运动边界上的真空和中心点处的奇异性所引起的强非线性。
This paper is concerned with the Newtonian limit of the relativistic Euler-Poisson equation. Under conditions of the free boundary and vacuum, we prove the existence and uniqueness of local smooth solutions, which converge to the solutions of the classical Euler-Poisson equation at the rate of c− 2, where c is the speed of light. From the mathematical standpoint, we successfully overcome the strong nonlinearity caused by the Lorentz factor, the vacuum occurring on the moving boundary and the singularity at the center point by applying the weighted Sobolev space, respectively.