TY - JOUR T1 - On Compressible Smooth Viscous Fluids in Slowly Expanding Balls JO - Analysis in Theory and Applications VL - 1 SP - 28 EP - 65 PY - 2019 DA - 2019/04 SN - 35 DO - http://doi.org/10.4208/ata.OA-0001 UR - https://global-sci.org/intro/article_detail/ata/13091.html KW - Compressible Navier-Stokes equations, slowly expanding ball, weighted energy estimate, global existence. AB -

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].