具有真空和大振动的三维可压缩Navier-Stokes方程组的整体经典解和弱解
Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier-Stokes System with Vacuum and Large Oscillations
摘要：
我们建立了三维完全可压缩Navier-Stokes方程组的整体经典解的存在性和唯一性，该方程组具有光滑的初始值，具有小的能量，但在允许初始密度为零的情况下可能存在大的振荡.此外，对于可能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。这些结果推广了前人关于初始密度严格远离真空的经典解和弱解的结果，并且首次得到了具有大振荡和包含真空态的整体经典解和弱解的结果.
英文摘要：
We establish the global existence and uniqueness of classical solutions to the three-dimensional full compressible Navier-Stokes system 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 vacuum, and are the first for global classical and weak solutions which may have large oscillations and can contain vacuum states.
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