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

Anthony Suen

doi:10.3934/dcds.2020093

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2020, Volume 40, Issue 3: 1775-1798. Doi: 10.3934/dcds.2020093

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

Anthony Suen^,

Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong, China

^* Corresponding author: Anthony Suen
^* Corresponding author: Anthony Suen

Received: July 2019

Published online: March 2020

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

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