| Title:
|
Some recent results on the existence of global-in-time weak solutions to the Navier-Stokes equations of a general barotropic fluid (English) |
| Author:
|
Feireisl, Eduard |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
203-209 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This is a survey of some recent results on the existence of globally defined weak solutions to the Navier-Stokes equations of a viscous compressible fluid with a general barotropic pressure-density relation. (English) |
| Keyword:
|
compressible Navier-Stokes equations |
| Keyword:
|
global existence |
| Keyword:
|
weak solutions |
| MSC:
|
35A05 |
| MSC:
|
35D05 |
| MSC:
|
35Q30 |
| MSC:
|
76N10 |
| idZBL:
|
Zbl 1009.35061 |
| idMR:
|
MR1981525 |
| DOI:
|
10.21136/MB.2002.134172 |
| . |
| Date available:
|
2012-10-05T12:54:51Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134172 |
| . |
| Reference:
|
[1] S. N. Antontsev, A. V. Kazhikhov, V. N. Monakhov: Boundary Value Problems of Mechanics of Non-Homogeneous Fluids.Novosibirsk, 1983. (Russian) |
| Reference:
|
[2] R. J. DiPerna, P.-L. Lions: Ordinary differential equations, transport theory and Sobolev spaces.Invent. Math. 98 (1989), 511–547. MR 1022305, 10.1007/BF01393835 |
| Reference:
|
[3] B. Ducomet, E. Feireisl, H. Petzeltová, I. Straškraba: Global in time weak solutions for compressible barotropic self-gravitating fluids.Adv. Appl. Math. Submitted (2001). MR 1841897 |
| Reference:
|
[4] E. Feireisl: The dynamical systems approach to the Navier-Stokes equations of compressible fluid.Advances in Mathematical Fluid Mechanics, J. Málek, J. Nečas, M. Rokyta (eds.), Springer, Berlin, 2000. MR 1863209 |
| Reference:
|
[5] E. Feireisl: On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable.Comment. Math. Univ. Carolin. 42 (2001), 83–98. Zbl 1115.35096, MR 1825374 |
| Reference:
|
[6] E. Feireisl, A. Novotný, H. Petzeltová: On the domain dependence of solutions to the compressible Navier-Stokes equations of a barotropic fluid.Math. Meth. Appl. Sci (to appear). MR 1918742 |
| Reference:
|
[7] E. Feireisl, A. Novotný, H. Petzeltová: On the existence of globally defined weak solutions to the Navier-Stokes equations of compressible isentropic fluids.J. Math. Fluid Dynamics 3 (2001), 358–392. MR 1867887 |
| Reference:
|
[8] E. Feireisl, H. Petzeltová: On integrability up to the boundary of the weak solutions of the Navier-Stokes equations of compressible flow.Commun. Partial Differential Equations 25 (2000), 755–767. MR 1748351, 10.1080/03605300008821530 |
| Reference:
|
[9] P.-L. Lions: Mathematical Topics in Fluid Dynamics, Vol. 2, Compressible Models.Oxford Science Publication, Oxford, 1998. MR 1637634 |
| Reference:
|
[10] P.-L. Lions: Bornes sur la densité pour les équations de Navier-Stokes compressible isentropiques avec conditions aux limites de Dirichlet.C. R. Acad. Sci. Paris, Sér I. 328 (1999), 659–662. MR 1680813 |
| . |
