Volume 35, Issue 1
On Compressible Smooth Viscous Fluids in Slowly Expanding Balls

Huicheng Yin & Lin Zhang

Anal. Theory Appl., 35 (2019), pp. 28-65.

Published online: 2019-04

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  • 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].

  • Keywords

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

  • AMS Subject Headings

35L70, 35L65, 35L67, 76N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-35-28, author = {}, title = {On Compressible Smooth Viscous Fluids in Slowly Expanding Balls}, journal = {Analysis in Theory and Applications}, year = {2019}, volume = {35}, number = {1}, pages = {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].

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0001}, url = {http://global-sci.org/intro/article_detail/ata/13091.html} }
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].

Huicheng Yin & Lin Zhang. (2020). On Compressible Smooth Viscous Fluids in Slowly Expanding Balls. Analysis in Theory and Applications. 35 (1). 28-65. doi:10.4208/ata.OA-0001
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