摘要
In[17]and[19,20],the global existence and large time behaviors of smooth compressible fluids(including inviscid gases of Euler equations,viscous gases of Navier-Stokes equations,and rarified gases of Boltzmann equation,respectively)have been established in an infinitely expanding ball with a constant expansion speed.This paper concerns with the viscous fluids in a slowly expanding ball.By involved analy-sis on the density function and the weighted energy estimates,we show that the fluid in the slowly expanding ball smoothly tends to a vacuum state and there is no appearance of vacuum in any part of the expansive ball.Our present result is a meaningful supplement to the one in[19].
In [17] and [19, 20], the global existence and large time behaviors of smooth compressible fluids(including inviscid gases of Euler equations, viscous gases of Navier-Stokes equations, and rarified gases of Boltzmann equation, respectively) have been established in an infinitely expanding ball with a constant expansion speed. This paper concerns with the viscous fluids in a slowly expanding ball. By involved analysis on the density function and the weighted energy estimates, we show that the fluid in the slowly expanding ball smoothly tends to a vacuum state and there is no appearance of vacuum in any part of the expansive ball. Our present result is a meaningful supplement to the one in [19].
基金
supported by the NSFC (No. 11571177 and No. 11731007)
a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
