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

Anthony Suen

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arXiv · 2011.05656

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

Anthony Suen

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Abstract

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.

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Anthony Suen. 2020-11-11. Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy. https://arxiv.org/abs/2011.05656

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