On Compressible Smooth Viscous Fluids in Slowly Expanding Balls

Year:    2019

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 1 : pp. 28–65

Abstract

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].

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-0001

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 1 : pp. 28–65

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    38

Keywords:    Compressible Navier-Stokes equations slowly expanding ball weighted energy estimate global existence.