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.
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Early online date||Dec 2019|
|Publication status||Published - Mar 2020|
CitationSuen, 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
- Navier-Stokes-Poisson equations
- Compressible flow
- Blow-up criteria