Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier-Stokes System with Vacuum and Large Oscillations
Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier-Stokes System with Vacuum and Large Oscillations
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真空大振荡三维全可压缩纳维斯托克斯系统的全局经典弱解
DOI：
10.1007/s00205-017-1188-y
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发表时间：
2018
影响因子：
2.5
通讯作者：
Li Jing
中科院分区：
文献类型：
--
作者：
Huang Xiangdi;Li Jing
对于三维完全可压缩Navier-Stokes方程组，在光滑初值条件下，当初始密度为零时，我们得到了该方程组经典解的整体存在唯一性.此外，对于不连续且含有真空态的初值，我们还得到了整体弱解的存在性。这些结果推广了以前的经典和弱解的初始密度是严格远离真空，是第一个整体的经典和弱解，可能有大的振荡，可以包含真空状态。
For the three-dimensional full compressible Navier–Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid, we establish the global existence and uniqueness of classical solutions with smooth initial data which are of small energy but possibly large oscillations where the initial density is allowed to vanish. Moreover, for the initial data, which may be discontinuous and contain vacuum states, we also obtain the global existence of weak solutions. These results generalize previous ones on classical and weak solutions for initial density being strictly away from a vacuum, and are the first for global classical and weak solutions which may have large oscillations and can contain vacuum states.