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We are concerned with global finite-energy solutions of the three-dimensionalcompressible Euler-Poisson equations with {\it gravitational potential} and{\it general pressure law}, especially including the constitutive equation of{\it white dwarf stars}. In this paper, we construct global finite-energysolutions with spherical symmetry of the Cauchy problem for the Euler-Poissonequations as the inviscid limit of the corresponding compressibleNavier-Stokes-Poisson equations. The strong convergence of the vanishingviscosity solutions is achieved through entropy analysis, uniform estimates in$L^p$, and a more general compensated compactness framework via several newmain ingredients. A key estimate is first established for the integrability ofthe density over unbounded domains independent of the vanishing viscositycoefficient. Then a special entropy pair is carefully designed via solving aGoursat problem for the entropy equation such that a higher integrability ofthe velocity is established, which is a crucial step. Moreover, the weakentropy kernel for the general pressure law and its fractional derivatives ofthe required order near vacuum ($\rho=0$) and far-field ($\rho=\infty$) arecarefully analyzed. Owing to the generality of the pressure law, only the$W^{-1,p}_{\mathrm{loc}}$-compactness of weak entropy dissipation measures with$p\in [1,2)$ can be obtained; this is rescued by the equi-integrability of weakentropy pairs which can be established by the estimates obtained above, so thatthe div-curl lemma still applies. Finally, based on the above analysis of weakentropy pairs, the $L^p$ compensated compactness framework for the compressibleEuler equations with general pressure law is established. This new compensatedcompactness framework and the techniques developed in this paper should beuseful for solving further nonlinear problems with similar features.

Global Finite-Energy Solutions of the Compressible Euler-Poisson Equations for General Pressure Laws with Spherical Symmetry