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

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Abstract

We study the low-energy solutions to the 3D compressible NavierStokes-Poisson equations. We first obtain the existence of smooth solutions with small L²-norm and essentially bounded densities. No smallness assumption is imposed on the H⁴-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 R³. We also provide a blow-up criterion of solutions in terms of the L-norm of density. Copyright © 2019 American Institute of Mathematical Sciences.
Original languageEnglish
Pages (from-to)1775-1798
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume40
Issue number3
Early online dateDec 2019
DOIs
Publication statusPublished - Mar 2020

Citation

Suen, A. (2020). Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy. Discrete and Continuous Dynamical Systems- Series A, 40(3), 1775-1798. doi: 10.3934/dcds.2020093

Keywords

  • Navier-Stokes-Poisson equations
  • Compressible flow
  • Blow-up criteria

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