On the Global Motion of Viscous Compressible Barotropic Flows Subject to Large External Potential Forces and Vacuum
On the Global Motion of Viscous Compressible Barotropic Flows Subject to Large External Potential Forces and Vacuum
复制标题
DOI：
10.1137/130941298
复制
发表时间：
2015-03
期刊：
影响因子：
--
通讯作者：
Jing Li;Jianwen Zhang;Junning Zhao
中科院分区：
文献类型：
--
作者：
Jing Li;Jianwen Zhang;Junning Zhao
研究了三维可压正压Navier-Stokes方程在大外力作用下的Cauchy问题。我们首先证明了Cauchy问题存在唯一的整体强解，在初始值能量较小且唯一的稳态严格远离真空的条件下，该解具有大的振荡和内部真空.其次，我们证明了如果初始数据更正则，并满足一些额外的相容性条件，强解确实是一个经典的远离初始时间。最后，作为副产品，还得到了具有大的外部势力和间断的初始数据包含真空的弱解的整体存在性和大时间行为。
We study the Cauchy problem of three-dimensional compressible barotropic Navier--Stokes equations with large external potential forces. We first prove that the Cauchy problem has a unique global strong solution with large oscillations and interior vacuum, provided the initial data are of small energy and the unique steady state is strictly away from vacuum. Next, we show that if the initial data are more regular and satisfy some additional compatibility conditions, the strong solution is indeed a classical one away from the initial time. Finally, as by-products, the global existence and large-time behavior of weak solutions with large external potential forces and discontinuous initial data containing vacuum are also obtained.