Abstract
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.
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