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The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball, Ⅱ: 3D Navier-Stokes equations

  • * Corresponding author: Huicheng Yin

    * Corresponding author: Huicheng Yin 

The authors were supported by the NSFC (No.11571177, No.11731007) and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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  • We concern with the global existence and large time behavior of compressible fluids (including the inviscid gases, viscid gases, and Boltzmann gases) in an infinitely expanding ball. Such a problem is one of the interesting models in studying the theory of global smooth solutions to multidimensional compressible gases with time dependent boundaries and vacuum states at infinite time. Due to the conservation of mass, the fluid in the expanding ball becomes rarefied and eventually tends to a vacuum state meanwhile there are no appearances of vacuum domains in any part of the expansive ball, which is easily observed in finite time. In this paper, as the second part of our three papers, we will confirm this physical phenomenon for the compressible viscid fluids by obtaining the exact lower and upper bound on the density function.

    Mathematics Subject Classification: 35L70, 35L65, 35L67, 76N15.


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  • Figure 1.  A viscous fluid in a 3-D expanding ball

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