Singular behavior of vacuum states for compressible fluids
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 211-231 |
| Journal / Publication | Journal of Computational and Applied Mathematics |
| Volume | 190 |
| Issue number | 1-2 |
| Publication status | Published - 1 Jun 2006 |
Conference
| Title | International Conference on Mathematics and its Application |
|---|---|
| Period | 28 - 31 May 2004 |
Link(s)
Abstract
In this survey paper, we will present the recent work on the study of the compressible fluids with vacuum states by illustrating its interesting and singular behavior through some systems of fluid dynamics, that is, Euler equations, Euler-Poisson equations and Navier-Stokes equations. The main concern is the well-posedness of the problem when vacuum presents and the singular behavior of the solution near the interface separating the vacuum and the gas. Furthermore, the relation of the solutions for the gas dynamics with vacuum to those of the Boltzmann equation will also be discussed. In fact, the results obtained so far for vacuum states are far from being complete and satisfactory. Therefore, this paper can only be served as an introduction to this interesting field which has many open and challenging mathematical problems. Moreover, the problems considered here are limited to the author's interest and knowledge in this area. © 2005 Elsevier B.V. All rights reserved.
Research Area(s)
- Boltzmann equation, Euler equations, Euler-Poisson equations, Navier-Stokes equations, Vacuum singularity
Citation Format(s)
Singular behavior of vacuum states for compressible fluids. / Yang, Tong.
In: Journal of Computational and Applied Mathematics, Vol. 190, No. 1-2, 01.06.2006, p. 211-231.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
