Article Contents
Article Contents

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

• * Corresponding author: Anthony Suen
• 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.

 Citation:

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