| Title:
|
A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid (English) |
| Author:
|
Novo, Sébastien |
| Author:
|
Novotný, Antonín |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
331-339 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz. (English) |
| Keyword:
|
Navier-Stokes equations |
| Keyword:
|
compressible fluid |
| Keyword:
|
weak solution |
| MSC:
|
35D05 |
| MSC:
|
35Q30 |
| MSC:
|
76N10 |
| idZBL:
|
Zbl 1099.35088 |
| idMR:
|
MR2151460 |
| DOI:
|
10.1007/s10492-005-0026-y |
| . |
| Date available:
|
2009-09-22T18:22:45Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134610 |
| . |
| Reference:
|
[1] M. E. Bogovskiĭ: The solution of some problems of vector analysis, associated with the operators div and grad.Trudy Semin. S. L. Soboleva 1 (1980), 5–40. (Russian) MR 0631691 |
| 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] L. C. Evans, R. F. Gariepy: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics.CRC Press, Boca Raton, 1992. MR 1158660 |
| Reference:
|
[4] P.-L. Lions: Mathematical Topics in Fluid Mechanics, Vol. 2. Compressible Models. Lecture Series in Mathematics and its Applications.Clarendon Press, Oxford, 1998. MR 1637634 |
| Reference:
|
[5] S. Novo, A. Novotný: On the existence of weak solutions to the steady compressible Navier-Stokes equations when the density is not square integrable.J. Math. Kyoto Univ. 42 (2002), 531–550. MR 1967222, 10.1215/kjm/1250283849 |
| Reference:
|
[6] S. Novo, A. Novotný: On the existence of weak solutions to the steady compressible Navier-Stokes equations in domains with conical outlets.J. Math. Fluid Mech. 7 (2005), 1–24. MR 2220444 |
| . |
