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Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy

  • * Corresponding author: Anthony Suen

    * Corresponding author: Anthony Suen
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  • We study the low-energy solutions to the 3D compressible Navier-Stokes-Poisson equations. We first obtain the existence of smooth solutions with small $ L^2 $-norm and essentially bounded densities. No smallness assumption is imposed on the $ H^4 $-norm of the initial data. Using a compactness argument, we further obtain the existence of weak solutions which may have discontinuities across some hypersurfaces in $ \mathbb R^3 $. We also provide a blow-up criterion of solutions in terms of the $ L^\infty $-norm of density.

    Mathematics Subject Classification: Primary: 35Q30; Secondary: 76N10.


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