论文标题
具有有限能量的3D可压缩Navier-Stokes-Poisson方程的解决方案的存在和爆炸标准
Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy
论文作者
论文摘要
我们研究了3D可压缩的Navier-Stokes-poisson方程的低能解决方案。我们首先获得了具有小$ l^2 $ norm和本质上有界密度的平滑溶液的存在。对初始数据的$ H^4 $ norm施加了很小的假设。使用紧凑的参数，我们进一步获得了弱解决方案的存在，这些解决方案可能在$ \ mathbb {r}^3 $中的某些Hypersurfaces中存在不连续性。我们还根据$ l^\ infty $ norm的密度提供了解决方案的爆炸标准。
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.
