| Title:
|
On weak solutions of steady Navier-Stokes equations for monatomic gas (English) |
| Author:
|
Březina, J. |
| Author:
|
Novotný, A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
611-632 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We use $L^\infty$ estimates for the inverse Laplacian of the pressure introduced by Plotnikov, Sokolowski and Frehse, Goj, Steinhauer together with the nonlinear potential theory due to Adams, Hedberg, to get a priori estimates and to prove existence of weak solutions to steady isentropic Navier-Stokes equations with the adiabatic constant $\gamma>{1\over3}(1+\sqrt{13})\approx 1.53$ for the flows powered by volume non-potential forces and with $\gamma>{1\over8}(3+\sqrt{41}) \approx1.175$ for the flows powered by potential forces and arbitrary non-volume forces. According to our knowledge, it is the first result that treats in three dimensions existence of weak solutions in the physically relevant case $\gamma\le{5\over3}$ with arbitrary large external data. The solutions are constructed in a rectangular domain with periodic boundary conditions. (English) |
| Keyword:
|
steady compressible Navier-Stokes equations |
| Keyword:
|
periodic domain |
| Keyword:
|
isentropic flow |
| Keyword:
|
existence of the weak solution |
| Keyword:
|
potential theory |
| MSC:
|
35D05 |
| MSC:
|
35Q30 |
| MSC:
|
76D05 |
| MSC:
|
76N15 |
| idZBL:
|
Zbl 1212.35345 |
| idMR:
|
MR2493941 |
| . |
| Date available:
|
2009-05-05T17:13:26Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119749 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
