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 - <p style="text-align: justify;">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].</p>